No. Because "supports the confederacy" isn't a protected class.
As far as US law goes, you can generally refuse a service to anyone for any reason, unless that reason is related to a protected class to which the person belongs, unless you have some other exception (almost always religious) for not doing the thing.
Protected class does also not mean that everyone else if a free target for discrimination, and for international companies there is the European Convention on Human Rights. Refusing service based on politics require the company to do a quite complicated dance around a long list of laws and I doubt any company lawyer would be very happy to give a green light for it.
This is a fun game! Suppose the baker is Muslim and you ask for a cake with a cartoon of The Prophet? Wouldn’t that make you the bigot?
My point is you can contrive any example here to get the conclusion you want.
I would want the black baker owner to be able to not only refuse to bake the cake, but to also tell the customer to take a hike and never return.