One more reference on this thing about "religious liberty", cake bakers, and gay marriage.

There is a very good article by Mark Reiff published in July in The Conversation here https://theconversation.com/a-philosopher-argues-why-no-one-has-the-right-to-refuse-services-to-lgbt-people-80365 .  He writes about liberties versus rights.  He outlines three kinds of liberty:  negative liberty, positive liberty, and republican liberty.  (The "republican" does not refer to the political party of that name but to the form of government we claim to have.)

Not all liberties are protected by rights.  Especially when one person's "liberty" infringes on the "liberty" of another.  And that is where republican liberty protects people against arbitrary treatment. "the refusal of service to gay couples is itself an arbitrary act. It is an act of domination – just like refusal of service to black or Jewish people or inter-racial couples."

Well worth the read.