And this is exactly why Obama's side is right.Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
When employers are forced to give contraception to their employees, it does not in the slightest undermine their freedom of religion. How do you know they'll actually be used for contraception? How do you know if they'll be used at all? Unless the employers can prove that it is directly and purposely being used to undermine their organization, no freedom of religion is undermined here.
At the same time, the employee has the right to freedom of religion. This could be catholicism, but it could just as well be agnosticism or atheism. If an employee wants to use contraception despite what catholicism says, freedom of religion dictates that this should be possible. If not, this is 'prohibiting the free exercise thereof'
The religious organizations are currently trying to exert dominance through paternalistic behavior. The lives of the people who are in these religious organizations are none of their business. As such, they are trying to take much more than they have the right to.
You either let employers give contraception to everyone or you don't let them give it at all, making an exception for religious organizations is discrimination.