No they don’t.
Only protected groups can be discriminated against.
A Christian anti-gay marriage group that wanted a gay baker to produce a cake for their event could be turned down without consequence.
Nazis and Christians aren’t protected groups.
You know, everybody is missing the main point here. It’s that the government is deciding who is and is not part of a protected group.
Of course, it’s been doing that for at least 50 years now.