"What's stopping them" is apparently that pesky ideal of non-discrimination in the public arena as mandated by law.  Making that cake or providing the license for the gay wedding, allowing females unobstructed and peaceful access to health clinics, as well as the freedom to make health decisions according to their own consciences, even allowing some to use public rest rooms as they choose -- all have a basis in discrimination.  We see this practiced time after time as the "right to discriminate" is upheld for our own religious schools and institutions despite numerous employment laws applicable to the general public.  

I don't think I'll ever understand why some think these laws simply don't apply to them, particularly when such effort is made in the legislative process to mitigate probable impact against personal conscience matters.  The Little Sisters' refusal to sign a simple form is the perfect illustration of the pinnacle of nonsensical legal shenanigans.  Blecch!