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.