Separation of Church and State

I was reading this article about House Speaker John Boehner making a huge fuss about the White House’s stand on providing equal access to birth control to all women.

Now, I’m no contitutional scholar, but it seems like there are two interpretations of “Separation of Church and State”. The Democrats (for the most part) view it as “Keep matters of faith and religion separate from policy.” While the GOP (for the most part) view it as “Support Christianity – and *only* Christianity – using the full power of policy to do so.”

I may be generalizing, but whenever government supports an idea that benefits society as a whole (such as preventing unwanted pregnancy in this case), the other side (the GOP in this case) claim that government is stepping on religious freedom/rights/whatever. Isn’t the idea that policy be separate from religion? Isn’t America a great melting pot?