Does your imaginary baker provide hate-speech cakes to other haters? Then yes, if their normal line of products includes hate speech then they can't discriminate on the kind of hate speech. (I'm ignoring more complex legal issues relevant to hate speech, and protected class issues, in order to play out your analogy and show you why it's wrong. I could make those arguments as well, but I'm picking the simplest one.)

Your baker could have a policy of baking NO hate-speech cakes, then no one can compel them to put their hate on a cake. See the problem with your analogy now? 

This baker makes wedding cakes, and he's in a business of public accommodation, that means his choices are bake wedding cakes for everyone, or don't bake any wedding cakes. If he provides a service he has to provide it to everyone (except for legitimate denial of service, which is spelled out in public accommodation laws).

And my new band name: "Hate on a Cake".