Not only is it possible the baker will win. It is fairly likely he will win.
To me it would be a clear violation of law if the baker were, for instance, to refuse to serve gay people at all. If he put a big sign on his door that said we will not serve gay people I don't think that would be allowed even though the civil rights act doesn't technically protect sexual orientation. Here the baker is refusing to make a custom cake for a gay wedding. He isn't discriminating against gay people generally. He is refusing to bake a cake customized to celebrate two gay people getting married. Would you, for instance, require a Jewish baker to bake a cake for a mosque that wanted to hold a religious ceremony celebrating a verse in the Koran that proclaims Jews should be harmed? The only people being impacted by the choice of the baker are Muslims. But that does not mean the baker would refuse to provide service to Muslims at all - just that he would not make that particular customized cake.
There is one interesting precedent from many years ago where a person who ran a wedding chapel refused to personally perform wedding ceremonies for mixed race couples on religious grounds. He would allow other clergy to use his facility and perform such ceremonies. But he personally refused to participate. He was rung up on charges for refusing to perform a ceremony. He won.
This particular case is, admittedly, different in several ways from that case. But that case highlights how this case is not cut and dry.
