The debate actually centers on where the line between religious freedom and a citizens' secular obligations to society should be drawn. This is not a Constitutional issue, but a less glamorous and equally compelling statutory issue.
Long life and lots of experience have taught me that nobody ever changes their mind about abortion. But to put a face, or at least a name, on the subject, here's a story: Fifty-three years ago when I was 16, I had an abortion.
There is nothing in the mandate that forces the religious to take contraceptives or to condone contraception. It's a requirement that anti-contraception communities accept the practices of other communities, like the Amish having to accept that not everyone else travels in a horse-drawn buggy.