Here's what Republicans have to do to become relevant again: Get out of every woman's doctor's office. I've had my fair share of long term relationships, so I'm solely going on the women I've been with, but a full half of them were unable to use the typical inexpensive birth control. One was because she was hypoglycemic, another was because of thyroid issues, etc..
The question isn't complicated: Should insurance as a baseline part of coverage include birth control, which insurance COMPANIES want to do by the way because it reduces long term costs, or should corganizations be able to enforce their morality on the available healthcare plans that employees or students have to pay for. The aggregate effect of making the birth control available is better health results over the long term, less expensive insurance, less unwanted pregnancies, fewer abortions. The aggregate effect of the opposite is to give theocrats a smug sense of satisfaction. Which of those two do you value more?