The baker will bake a cake for the people, just not one with a theme that clashes with their personal values. This situation is more like refusing to bake a Kwanzaa cake than denying African Americans service. Or maybe a baker campaigned for Hillary, and is now refusing to bake a "Make America Great Again" Trump cake.
From a religious angle, there are lots of things that religions handle differently. I shouldn't be able to force a Muslim to serve me pork and alcohol, for instance. I also shouldn't be able to force a Jewish wood carver to carve a manger scene if they don't want to. Not baking a gay-themed wedding cake falls along those lines. Great injustices have been committed against gay people, but this isn't one of them.
If the baker loses, then people will have government backing to force artists to take all kinds of commissions that they disagree with. For those who wish "clean" furry artists would draw more porn, your dreams may soon come true! If the ruling is to be applied evenly, they will be forced to accept commissions that go against their conscience.