Yes you are right. But I think it is even simpler than that. The reason doesn’t matter. Religious objection to me is besides the point. To me it is simple age old common law. Two people must willingly enter into a contract. The reason one party doesn’t wish to enter into a contract is irrelevant.
Putting a cake on the shelf of a public establishment is “an offer for sale” and the terms are usually posted such as hours of operation and which forms of payment they accept. The second someone walks in and says “I’ll buy it” the offer is accepted and the contract is done.
But open to the public does not mean you have to accommodate any special request any member of the public asks. There could be 15 reasons why the baker refuses to make a specific cake. It is silly to even argue the question that his refusal is based on hatred or religion or any other issue. He cannot be compelled, period.
Just to be clear, I mean to say that the cake on the display case is offered for sale “as is” and per the posted policies. If the store had a sign that said “we will write anything you want on the cake for 20 cents per character” then the baker would have to write whatever the customer asked. But generally, the cake on display is offered for sale as-is and must be sold as-is to anyone who agrees to the posted terms. The baker cannot be compelled to do anything he does not want to do if he did not already offer to do it.