Why do you think it's a given that anti-censorship common-carrier regulation would have an exception for "hate speech"? There's no constitutional precedent for that. There are specific categories of speech that the government may restriction --- slander and obscenity, for example --- and so-called "hate speech" isn't on the list. The United States has a very strong protections for free speech, even speech that offends people. Social media can, will, and must be legally required to carry everyone's speech, even when that speech is offensive.
Social media is exactly like a railroad. It's infrastructure marketed to the general public as an important part of participating in society. Unelected and unaccountable individuals in Bay Area meeting rooms do not get to unilaterally decide how the rest of the world may speak.