Good question. It depends on the law.
The US has civil rights laws that prevent businesses from discriminating on the basis of race, sex, age, religion or disabilities. Some states also protect sexual orientation. So it depends on why you don't want to bake the cake.
No state, and definitely not the federal government, bars discrimination based on political ideology. If you want to do that you'll need to update the civil rights laws.
So my rights are dependent on my intentions? And here I thought they were granted by God himself and were inalienable.
The point is, as it stands now, private property means nothing to the government. If you are “in public” I guess your freedom of Association is curbed? If I have Freedom of Asssociation, then I can discriminate all I want, in theory. But that is not the case. The point that I am making is that at this time the Left determines how the Constitution is followed.