Thank you for your very well researched and reasoned disagreement. It's frankly a breath of fresh air, and I can't really say that you're wrong on any specific point.
I think the fundamental issue in the US right now is not an overall shift in public opinion, but rather a polarization. It's a super weird polarization, because none of the significant poles (I think there are at least four) are ideologically consistent. Nor do any benefit any particular cohesive group. Such is the nature of coalition politics in the information age.
When two sides are so far apart on an issue, it becomes very difficult to have a constructive debate. When something is difficult, it's only human nature to find a different way to accomplish the same goal. Censorship is one way to do that: leveraging resources outside the debate in an attempt to make your opposition less effective.
That being said, I think some of the reaction to this is overstated. People are often quick to cry censorship at someone else's act of using his or her own free speech in response, e.g. the "no-platforming" stuff you refer to. Citizens United v. FEC held that corporations, being made up of individuals, have very similar free speech rights to those of individuals. It's not a stretch to extend this to editorial discretion, which means that these companies do indeed have that discretion.
Yet two of the major poles that I identify largely agree with the no-platforming of hate speech, and disagree with the decision in Citizens United v. FEC. The other two agree with Citizens United v. FEC, and disagree with no-platforming of hate speech. These are based on the same principle, but to a good first approximation, nobody is consistent in that principle.
I'm not totally sure where we go from here, but it's sure to be interesting (in the sense of the apocryphal Chinese curse).