I don't think it's fair to call this phenomenon "leftwing". My perception is that those who advocate deplatforming/censorship are centrists who call themselves "progressives". They do this mostly in order to support existing power structures that they fear are threatened by free speech. Very few actual leftists in the American context are against free speech.
I wanted to stress that I didn't mean it as a leftwing phenomenon. It's just that the GP seemed to describe it as a peculiarly rightwing one, and I think we've seen instances on the left as well (particularly recently). And while the left is generally much more averse to physical violence than the right, it's also more socially accepted and mainstream, so the outrage storms are more pronounced and the calls for censorship and sometimes criminalisation meet much less resistance.
I didn't agree with your first comment above, as I mostly focus on violent extremism, but you do raise a good point about the general intensity of polarization and how there is certainly support on the left for social sanctions against those we disagree with.
I don't exactly subscribe to the proposals in your example article, but I do think that climate denial is a sort of fraud which has real externalities, and have suggested that people should listening to or engaging with known climate deniers. It seems to me that there's something fundamentally wrong with the idea that it's OK to lie about products or policy for the sake of profit and then assign blame to the victims of predictable externalities for their credulity or lack of preparedness.
One thing we've learned in the age of social media is that false information is considerably more likely to go viral than true information- good news for the entertainment industry, less good in areas like public health or policymaking. It's likely that the ease of transmission is that false information tends to leverage easy prior assumptions over difficult unintuitive ones such that cognitive bias could be said to yield a 'liar surplus' which has an economic value to the deliberate proponent of untruth. It's possible that this will lead to the development of weighting tools for assessing the reliability of information through analysis of the rate and direction of its transmission, but as long as it's profitable to sell false information we will continue to get more of that.
