That the provision requiring providers to violate their religious beliefs in order to pay for employees' birth control itself is in blatant violation of the First Amendment seems not to matter.
C'est la vie. Unless the Supreme Court completely loses all sense of what the Constitution actually says (as opposed to what the justices would like it to say), that provision of Obamacare is going to be thrown out regardless of the narrow point on which the Missouri ruling was made (namely, that Federal law supersedes state law).
The contortions the Left goes through on this and similar issues are truly amazing. Any way you look at them, they come down to insisting that the First Amendment is unconstitutional.