It's pretty well established First Amendment/constitutional law that the "state" has the ability to regulate secular activities of a so-called religious group.
I had posited a question in one of my responses - should a Christian Science group have the ability to only provide health insurance for prayers? Should Seventh Day Adventists/Jehovah Witnesses have the right to exclude blood transfusions.
I'm not stating that anyone must feel or think the same way I do. I'm merely stating that imposing regulations on the sectarian activities of a religious body is not a violation of the First Amendment.
I posited a theory as to why more people are not "outraged" by Catholic employers being required to have the same basic health care as anyone else and thought it might be because most people actually want birth control to be covered for anyone who wants it. Perhaps that's not the reason but in any event there certainly wasn't any kind of grass movement against the HHS requirement because I don't think most people find it problematic. If they did, wouldn't they have risen in an uproar as they did last week?
Religions have a right to practice their "religion" as it pertains to their religion. When they venture into sectarian pursuits, they become subject to the same laws as other entities and have no more right to defy the law than any other entity. The First Amendment merely prohibits government from restricting the exercise of religion - as it has been interpreted the government can make religious entities subject to sectarian laws when engaged in sectarian activities. And actually they can go further as in banning polygamy which was upheld by the SC in the early 20th century.