At the risk of being Captain Obvious a second-Religious liberty should not be an issue of what you prevent access to, or forbid. In other words Christianity (Not even those fire breathing Baptists) have no right to refuse general access to anything by way of contraception.

Religious freedom means Christians are free to refrain if they choose from extra marital sex. So those Christians can just not partake of contraception, abortion etc. Atheists are free to do as they please. The very idea that making some optional medicine or procedure available, even subsidized is not an encroachment at all.