Dennis I think you are probably a good guy who is trying to have a civilized conversation and keep an open mind. You're to be congratulated for that. But on the issue of who is attempting to shut down free speech the facts are against you.
And the left, what used to be the classic liberal left, has been taken over by some very extreme people. It has been coming for a long time now, decades, and while there may be a lot of people who consider themselves on the left, people who disagree with the new left extremism, they don't really count as representing the left if they just keep their mouths shut and allow it to happen.
There may be extremists on the right - although on free speech I haven't seen it - but they tend to get disavowed. One major difference that I see between left and right is that the left tries to enforce a monolithic set of values/rules and the right really doesn't do that (it's pretty hard to do that with people who put a high value on individualism).