Since no one answered your question about how much due process is needed, let me take a stab at it. To paraphrase the article, due process requires that the rules be known in advance, and that they be applied non-arbitrarily to each accused violator. I would also add that the rules should be as specific as possible, since vague terms like "hateful ideology" can be applied to almost anything controversial.

So for example, if an organization was going to censor certain political websites, they should specify precisely what is not allowed: Advocating socialism? The killing of non-combatants? etc.

If the rules are only going to be applied at the whims of the Twitter mob, then that should be posted in advance: "You will be in violation if you advocate for race-based killing AND there are at least 10,000 tweets in a single day condemning you."