Has this not been to the Supreme Court yet? I thought it had. (I've not read the article, I assume the link description is reasonably accurate) A plain cake is a commodity. A decorated cake is a piece of art and protected by the 1st Amendment; seems like a slam-dunk case. I don't think he has refused to bake an undecorated cake for anybody, just refuses to produce artwork celebrating their various perversions. And I assume he doesn't expect or demand anyone celebrate whatever his sins are.
He has been to the high court, but they're ruling was um, not exactly a full-throated defense of his right not to be press-ganged into service by roving packs of left-wing bigots. Which is why the roving packs of left-wing bigots are again attempting to press-gang him into service. cuz love is love, and diversity and stuff.
Oh, also according to some people that should know better, he asked for this, because he chose to be a baker. He should have known, all those years ago, that baking was a profession reserved for better and more open-minded people than he.
Being "open to the public" you see, must mean that one must do whatever one is asked to do, even if it's something everyone should know is morally wrong and a little stomach-turning.