The "bake" the cake argument is also misleading.

It's painted as if they refused to do any business with gay people. They were willing to sell them any of the cakes they baked. They didn't want to design a custom cake / do the art for it because it was against their religion. That's no different than demanding a Muslim draw a picture of Muhammed eating a hot-dog. Or better yet, forcing a gay cake decorator to decorate one with bible verses saying gay people are abominations.