What the heck is “the left” in this context? There is no organized left in the US, just a wacky amalgam of different kinds of people. If some students show up and protest a speaker, that’s what those students are doing. It’s not a sign of anything the overall left has done. Just like if some yahoos with guns show up they aren’t necessarily official representatives of the Republican Party.
If you want censorship and suppression of free expression, your best bet is the same as it’s always been – the religious right. They have always been the undisputed kings, and remain so today. I’m not interested in any discussion of “cancel culture” or freedom of speech, or the rest that doesn’t end “of course, as bad as the left can be, the right has always been worse.” Without that disclaimer, it’s just partisan yapping.