It would be unconstitutional, though a version this question is going before the Supreme Court right now in that case involving Christian bakers and gay wedding

It would be unconstitutional, though a version this question is going before the Supreme Court right now in that case involving Christian bakers and gay wedding cakes. I think the baker's lawyers are basing their argument on that sort of reasoning. I haven't followed the case closely enough to tell if that premise itself is actually in question, or if it's whether that premise is overridden by some other (e.g. regarding anti-discrimination laws).