You can have it both ways. Positions can be motivated either by process out outcome. A process position is "businesses should/should not be able to deny service to people based on <whatever dispute>". An outcome position is "We should protect gay couples and not white supremacists". You might not agree with the particular position, you might prefer developing supposedly content-neutral process positions, but many people think that the design of rules and systems is merely a means to getting to what they view as correct ends.

Your position is a bit like saying "Some people claim they're OK with the US/UK having nuclear weapons, but not North Korea. Can't have it both ways." or "Some people want charities to be tax exempt but not businesses. Can't have it both ways." or "Some people want gun control for civilians but not for the military. Can't have it both ways." Yes, many policies apply differently to different people for different reasons! That's a good thing.