Wrong. Obamacare requires people to pay for abortificients.
FWIW, I used to know some of the faculty at Baylor pretty well, and visited there fairly often for conferences and other reasons. I’m afraid I got the impression that Baylor is no longer a truly Christian university—especially at the top levels. It’s kind of the Notre Dame of Baptist universities.
Many if not most main line Christian churches do make a distinction between birth control and abortificients. The owners of Hobby Lobby reject abortificients.
The Catholic church has a different and valid argument of their own.
As has already been pointed out though, the real argument shouldn't be about either but about freedom from government tyranny.