I'll let the lawyers chat about the actual legal issues, though on these sorts of things I think it's mostly pointless. It ain't about the law, it's about the outcome. The issues are whether we privilege a specific set of supposedly Christian beliefs* (the Court would never do it for any of those other "fake" religions), and whether medical care for women is as important as medical care for men.
*Nor would they do it for most supposedly Christian beliefs, just the ones relating to restricting and punishing female sexuality, because that's all it's about anymore.
