Censorship is by its nature a political term: it is the removal of material that is considered to be obscene, politically unacceptable, or a threat to security. The phrase 'political censorship' is redundant, though perhaps not problematically so.
Here's what's clear: Twitter and Facebook have restricted access to this New York Post article (though I think Twitter may have backtracked on it). The question is whether their act was overtly political. There are two sides to this issue:
- The article itself makes claims about on a candidate for US President, and thus is prima faciafacie political speech. However...
- The article itself is misleading, conspiratorial, poorly substantiated, and in all ways of dubious credibility and merit.
The issue boils down to an unresolved legal question of whether acts of explicit libel against political figures are protected political speech. LBJ may have may have said that it is acceptable in politics to call your opponent a pig-f*cker just to force him to deny it, but this has never been addressed in court.
Further, as we all know, Twitter and Facebook are private companies, not government agencies, and have a right to censor content as they see fit. The only First Amendment issue here, in fact, lies in whether the Trump administration can use its power to force these private companies to publish information that goes against their internal policies. That is also an unresolved legal issue: whether the government can dictate and enforce the dissemination of propaganda through private media.
The unfortunate fact is that institutional norms that previously precluded this kind of behavior have fallen apart, and we do not have legal precedents that tell us how to cope with this new political reality.