They seem incapable of rational debate.
Now with the "they" again. I am part of the left, do you think I am incapable of rational debate?
I agree the "shouting down"/de platforming tactic is one predominantly found on the nut-left. But it is a propaganda strategy every bit as much as the current administration's attack on objective reality/facts. I think the reasonable response is to have a conversation about what constitute rational arguments/debate and then identify that where we see it. For instance, another strategy is trolling, something mostly found on the nut-right side of the issue.
I think you would have been surprised how closer my views were to your own just a few years ago.. but it was when I began reading the more islam/left-critical sources I began noticing inconsistencies and double standards were rampant.
When you find a critique leveled against the left, try to consider what general rule of discourse that critique assumes and then see how well other arguments from the same source stack up against that rule.
For instance, you are probably aware of the "special snowflake" meme/joke that is making the rounds, the "oooh I shouldn't hurt your feelz" kind of response. Well, Spicer just told us the president was getting demoralized by all the mean things people were saying about him but that one kind of got a free pass :-).
I mean this IS funny:
“And it’s unbelievably frustrating when you’re continually told it’s not big enough; it’s not good enough. You can’t win.”
I hear they can operate for that!
I bet if someone said that we shouldn't hurt HILLARYS feelings THAT one would be in "this week in stupid!" and she got reasons to be a bit sad!