Libertarians believe that bigotry should be legal, because we want the bigots to out themselves. Personally, I want to know which bakers don’t want to bake cakes for gay couples so I can open up a non-bigoted bakery directly next door. Let’s allow those ideas to compete in a free market; I bet we’d eradicate that sort of thinking within a generation.
When an activity becomes illegal it only pushes the activity “underground,” or into a black market. We know this doesn’t eradicate a thing, but just keeps it under the surface to grow and fester outside of the eyes of “polite” society.
So, what is the libertarian solution? Allow these ideas to compete on the free market. I won’t give money to businesses I fundamentally disagree with. And neither should you. I’m happy to do business with folks who express tolerance as a core principal. It is, after all, their property.