I'm a little shocked reading the comments here, as I come to LessWrong to find people who are hyper rational and meta-critical. Yet nearly every comment seems to have accepted at face value that this is a real phenomena that is happening.
I'm not suggesting it's not happening, but I am unconvinced it is. To make the claim that "A distributed culture of leftists are destroying open dialogue in a free society", I have to evaluate that hypothesis against every other possible hypothesis which explains the data I'm seeing.
For example, an alternative hypothesis is that "Partisan actors are motivated to signal boost certain events which conform to a partisan message they're trying to promote causing it to seem like a huge problem"
Again, I'm not suggesting that this alternative hypothesis is correct either, though there is definitely some evidence for it as well. There's an entire multidimensional distribution of hypotheses that could potentially explain the data.
To evaluate whether this is even happening, a good epistemic approach would be to find a way to create a set of binary or interval questions which when combined captures the hypothesis space. Then to evaluate each independently. For example you could first identify how credible it is that a given individual sharing a "cancelling" meme is actually a leftist (age of account, network with well known and established metrics). Then use the same criteria to find non-cancelling leftists and derive a ratio. Then find the ratio under which leftists call for cancelling versus the rate at which those on the right report cancelling.
Part of the problem with evaluating this is that there's a ton of feedback loops and it's a complex system. Which is why it's important to try finding actual data instead of relying on news articles that are asserting that something is happening. Formulate hypotheses that match the actual known data, and aggressively discount the certainty of the hypotheses to account for your own unknown biases and lack of concrete information.
As far as moderated discussions. Bad actors (typically on the right) seem to intentionally try to find low moderation forums with the explicit intent of crowding out voices they disagree with. A lot of this has resulting in extreme moderation forums that only allow group think. Try to avoid both types of groups, and instead try contributing to groups that only enforce open discussion and civility. If you can't find one, start one. There are a ton of people who are finding themselves trapped in this dichotomy, and starving those other groups of people is the best way to counteract them.