I don't know about "general democratic principles" but I would include these as ideas valued by liberalism and not by leftism.
Fortunately, Ann Coulter or someone has plenty of outlets for her speech. And we've come a long way from Governor Ronald Reagan ordering UC Berkeley to cancel speakers because he didn't like what they had to say.
How have we “come a long way” from Reagan doing it? No-platforming actions don’t require the backing of a democratic majority. A few self-righteous people get going and no one wants to burn political capital objecting. Making the disinvitation button available to a wider population isn’t progress.
> That's not what I see happening, but sure, you can accuse other people of that if you like.
I've seen videos of it happening. Basically a speaker is invited to give a talk, but people who disagree with her crowd the auditorium and scream to prevent the talk from being given. The intention is not to "engage [or] defeat on rational grounds," but to shut down and exclude.
A lot of the people who have this done to them are in fact disagreeable, but that doesn't make the reaction less illiberal.