You could make the argument that the "socially liberal" side that wants to censor hate speech, but protect gay people from discrimination is logically consisten

You could make the argument that the "socially liberal" side that wants to censor hate speech, but protect gay people from discrimination is logically consistent. A social liberal could argue on the point of protecting the rights of a marginalized minority. By censoring (for example) calls for violence, social liberals are protecting the safety of the targeted group. By requiring a cake shop to serve gay couples (or interracial couples, to throw in another example), social liberals are protecting a marginalized minority's access to services.