how can you refuse to make a cake for someone’s wedding, if your business is making wedding cakes? - Slim it's just a bakery, their business is baking cakes, buns, rolls, etc.
In this instance, the baker had been asked to bake a custom made cake to others' specifications and the baker found certain details to go against personal beliefs.
Suppose the law had come down on the side of the gay couple, i.e. bakers were now compelled by law to make things specified by others that go against the baker's beliefs.
You could have the following situation ...
Racist white people go to a black-owned bakery. They order a cake, made to their own specifications. They want 'I love the South' on one side and a confederate flag on the other. On the top of the cake they want a noose and gallows, with a black figure dangling. They also want 4 or 5 white figures standing around, laughing, smiling and clapping.
As it stands, the black baker can legally refuse to make such a cake.
I don't want that law to change ...