The first birth-control-related thing I heard of dominionists attempting to get banned (well, other than abortion and birth control in general) was with the IUD--dominionists have pushed the belief since at least the 60's that the IUD is somehow an abortifacient because it prevents implantation.  (The medical definition of pregnancy, according to practically everyone outside of the dominionist community, is once a zygote actually implants.)  In fact, you can actually see an example of this at this pro-dominionist site.

(Dominionist groups, possibly uniquely, regard life as beginning when the egg and sperm meet--at conception--thus giving odd new life to Monty Python's song "Every Sperm Is Sacred".  This belief in "Every Zygote Is Sacred" goes, at times, to the downright bizarre in dominionist circles--including zygote adoption schemes promoting adoption of spare in-vitro fertilisation embryos as "snowflake babies".)

Partly as a result from dominionist pressure, and partly because of lawsuits over one particular IUD called the Dalcon Shield (of which a fair number of the lawsuits were at least supported by dominionist groups), there are presently only two IUD devices approved in the US for medical use.

Around this time, dominionist groups started pushing for "conscience clauses" in legislatures to allow doctors, nurses and religious hospitals to "opt out" of being made to perform or even learn about abortion.  Most states were happy to go along with this, figuring that secular providers would "fill the gap" so to speak.

Dominionist groups next (and this actually started in the mid to late 80's, to my recollection; I remember seeing this sort of stuff in the Kentucky Right to Life newsletters at this point) started targeting the birth control pill claiming both that it made women more promiscuous and that it, too, was an abortifacient because it can be used as a "morning after" pill.  The same dominionist site claims this not only about the birth control pill but about every hormonal method of birth control, including NorPlant and Depo-Provera.

This is when it started being an issue to people even aside from the "birth control" thing.

Firstly, birth control pills are used for things besides birth control.  One of the things birth control pills are used for is to regulate irregular periods; another is to deal with extremely heavy periods or extremely painful periods.  Another reason is for management in polycystic ovary disease, which is an endocrine disorder that causes many of the regulatory hormones to be out of whack.

Depo-Provera is increasingly being used as a treatment for people with mild endometriosis--a disorder where you have bits of uterine tissue where you shouldn't, and...well, everytime one is on the monthly, so to speak, those bits of tissue bleed, just like the rest of your uterine tissue.  One of the nicer things about Depo-Provera is you don't bleed for six months, and is a little less harsh than other medical treatments for endometriosis like, oh, Syntrel or having an ovariohysterectomy (both of which basically throw your body into early menopause).

Denying birth control pills to someone who has polycystic ovary disease can ultimately be life-threatening--among other things, diabetes and obesity are longterm consequences as well as, well, the ovarian cysts (which are incredibly painful, we're talking gallstone/kidneystone levels of pain, and can get HUGE).  Birth control pills are just about the only non-surgical option OUT there for polycystic ovary disease, and childbirth for people with polycystic ovary disease can itself be potentially life-threatening as well.

(Yes, I have a wee bit of a family history of PCS.  Couldn't you tell?)

A pharmacist has no way of really telling whether a script is for birth control or for another, legitimate, medical indication (such as PCS or for medical management of abnormal menstrual periods--some of which are precursors of PCS itself).  

Dominionist pharmacists apparently--if the dominionists (including my family, who has a known family history of PCS, has had my sister hospitalised with PCS, has had an 80 pound ovarian cyst removed from my grandmother before) I've known are any judge--don't care.  They're quite happy to let women live with the medical consequences, based on their actions.

A particular group of "pro-life" pharmacists, Pharmacists for Life International, along with other groups with names like Physicians for Life, are encouraging doctors to not write birth control scripts, and encouraging pharmacists not to fill them--even if for legitimate medical reasons.

Remember those "conscience clauses" I mentioned?  Well, a lot of them were written quite broadly to begin with, and dominionist groups started pressuring for pharmacists to be included as well (an area which is still a major part of lobbying on these groups' behalf).  This Washington Post article explains how broad these have become.

It was probably inevitable that dominionist pharmacists would start refusing to fill prescriptions and claiming "conscience clause" exemptions.  

This started really ramping up when Plan B (essentially a stronger version of the birth control pill designed as a morning after pill--essentially instead of taking the triple dosage recommended of stronger birth control, it's in one pill) was approved for prescription by the FDA.  

Plan B, much like the regular birth control pill, works by preventing the egg and sperm from meeting up in the first place.  (Some docs say it may prevent implantation as well, but this is controversial.)  The problem is, you have to take it within 72 hours for it to work, or you have to resort to actual abortifacients like RU-486 or traditional abortion (or methotrexate, which can also be used as an abortifacient--I'm actually surprised the pro-lifers haven't gone after its use, even though methotrexate is a cancer chemotherapy drug as well).

Dominionist pharmacists started not only refusing to fill scripts for standard birth control and Plan B, but in some cases refusing to give them back or even tearing up prescriptions in the face of the people in question.

More reports started filtering in--from even cities as large as Milwaukee, Wisconsin--of women being unable to get Plan B prescriptions filled at all within the 72 hour window.  (In fact, that case led to a lawsuit after the woman ended up becoming pregnant as a direct result.)  A rape victim was denied Plan B by a dominionist pharmacist. One Missouri woman is going to court in regards to the problem after a Target pharmacist refused to fill a prescription for Plan B and refused to refer her--and Target defended the pharmacist.  And so on.

In fact, the problem has become so common that the governor of Illinois passed an emergency executive order requiring all pharmacists in the state to either fill prescriptions or refer to pharmacists that will.  (At least four dominionist pharmacists have been suspended by Walgreens Pharmacies as a result of this, and the dominionists in turn are suing.)  Some states, aware of criticism, are requiring referrals in their "conscience clause" laws  At least one site is now specifically focusing on the problem of "pharmacist refusal".

The problem goes further.  Multiple FDA advisory panels have recommended to sell Plan B over the counter (thus getting around the entire problem of "pharmacist refusal" by dominionist pharmacists), but no progress has been made; in fact, the head of the FDA committee on reproductive health has changed no less than three times in the past year over the issue of Plan B, including the forced resignation of at least one head who was linked to dominionist groups and the resignation of a second official regarding delays on Plan B.

A lot of people have expressed legitimate concern that the "conscience clauses", taken to their ultimate extreme, could result in refusals of other products or even refusals to offer care to people whom dominionists disapprove of--gays, or non-dominionists, for that matter.

There are signs this is already happening.

Dominionists are even going further in some instances--one dominionist legislator has attempted to propose banning distribution of birth control on state college campuses under the old dominionist canard that the pill "increases promiscuity".

There are dominionist judges now that--in almost identical manner to the dominionist pharmacists--are refusing to hear "judicial bypass" cases in regards to minors seeking consent for obtaining abortion services (or in some cases even prescription birth control); in some cases, these are the only judges in their county authorised to hear such cases.  Reportedly this is also including legal emancipation cases, which has effects far beyond abortion (one common legal mechanism for kids escaping abusive households is to have a judge declare legal emancipation); of note, one of the judges in question is in Shelby County Tennessee, home of one of Love In Action's facilities.  (At least one person has successfully made a bid for legal emancipation on the mere threat of being sent by his parents to Love In Action's facilities; another person was granted a hearing in Georgia for emancipation but may have been kidnapped (against the judge's custody order) and transported back to the Love In Action facility after he had escaped.  That case is under legal investigation and involves the one minor still at the facility.)

Also, "conscience clauses" are expanding to other medications that dominionists disapprove of solely because they "prevent consequences of sexual misbehaviour and might encourage promiscuity".  

A promising vaccine against human papilloma virus or HPV--which is the cause of not only nearly all cervical cancer, but nearly all penile cancer in men--has been shown to be highly effective--but may never make it stateside because dominionist groups like the Family Research Council are already coming out in opposition because they claim it could increase promiscuity.

There is legitmate fear that an HIV vaccine will probably be opposed on similar grounds, should one ever be developed that is effective, based on how funding of condoms for HIV prevention is already opposed by dominionist groups in Africa (where HIV infection rates often approach 40-50% even in the heterosexual population).

Not only are pharmacists refusing to fill legitimate prescriptions for Plan B and even monthly birth control (based on urban legends in the dominionist community promoted by groups like Pharmacists for Life International claiming they are a form of abortion), not only is approval of a vaccine for HPV (which, incidentially, would be the first effective vaccine for cancer, as 99 percent of all cervical and penile cancer is caused by HPV) being fought by dominionist groups even as it has completed phase III trials (because HPV is a cause of genital warts)...

...but per this livejournal entry there are now reports that dominionist pharmacists are refusing to fill scripts for (and occasionally destroying the scripts for) any prescriptions they feel may be for an STD (in this case, this was for Valtrex, a medication that is used for herpesviruses in general):

I know a young woman who has the misfortune to have contracted genital herpes.

She is on a daily regimen of Valtrex to prevent symptoms from manifesting themselves.

Recently she took her prescription to a pharmacist who was apparently a fundamentalist Christian.

Not only did he refuse to fill the prescription, but he tore it up and handed it back to her, saying, "God is punishing you for your sin."

Genital herpes (herpes simplex II) is one of a family of anywhere between nine and twelve human herpesviruses, which include herpes simplex I (oral herpes--cold sores), herpes zoster aka varicella (cause of chickenpox and shingles when the varicella virus reactivates in adults), Epstein-Barr virus (aka mononucleosis--which has also been linked to Wilms tumour and Burkitt's lymphoma), cytomegalovirus (a common complication in HIV patients which can cause blindness), etc.

A very common reason for prescription of drugs like Valtrex besides genital herpes is for kids who are leukemic or have depressed immune systems to prevent complications from exposure to chickenpox--most of those kids also cannot have the chickenpox shot, as it's a live vaccine, and exposure to chickenpox can be life threatening; even adults who have never had the chickenpox who are exposed are typically given a course of varicella antiglobulin along with a course of Valtrex--in the hope that the VAB will prevent infection, the latter will hopefully make it less severe.  (Chickenpox reactivating in adults can cause shingles, which is quite painful (and another reason why Valtrex is prescribed); in adults full blown chickenpox commonly hospitalises people and even kills them--Hawaii state legislature representative Patsy Mink died from chickenpox pneumonia as a result of catching it as an adult.)  

Another reason that Valtrex is prescribed is--interestingly--cancer. (Yes, seriously.)  As it turns out, Kaposi's sarcoma is (much like cervical cancer and penile cancer) one of the few cancers definitely linked to a virus--specifically, human herpesvirus 8.  Ironically, it was partly because of so many HIV patients getting Kaposi's sarcoma that doctors realised it was a virally caused cancer, and we can now treat it using drugs that attack other herpesviruses (including Valtrex).  

Valtrex is also prescribed to patients with particularly severe cases of mono or who are subject to severe complications from mono (for example, people who have had to have their spleens surgically removed).

Related drugs to Valtrex, and occasionally Valtrex itself, are also used in people who are exposed to non-human herpesviruses.  (Generally herpesviruses that are not fatal to other primates are fatal to humans and vice versa; herpesvirus B, which occurs in macacques, is almost invariably fatal in humans without immediate treatment with anti-herpetic antivirals like Valtrex and ganciclovir.  In fact, in many zoos and research facilities, it is standard procedure that if more than one monkey dies in a 24 hour period or if monkeys die after seeming ill all workers who worked with them go on immediate preventive courses of Valtrex in case the monkey had herpesvirus B.  It's considered that dangerous to people.)

Also, an increasing fear is that dominionists will start refusing to give antiretroviral drugs to HIV patients because they "disapprove of their lifestyle".  In fact, there are hints that the same dominionist groups behind "conscience clauses" are already linking birth control pills and HIV, and as dominionist groups are explicitly trying to expand "conscience clauses" in regards to funding related to HIV.