They should have to choose between neutral publishing and liability on their networks. If they want to censor then section 230 of the communications decency act should be repealed and let them take ownership of their decisions.

As it stands now they get zero liability for speech they can clearly police. I see hate groups in Facebook that Facebook doesn't close if reported. Let them own it

They're not forced to distribute it any more than they're forced to distribute content they do agree with.

In both cases, they're already providing the service to distribute it; they're simply leaving it alone and not acting at all.

Incidentally that's the best way for them to retain their Section 230 protection -- neutrality.