Its important to first set out what we mean by “right-wing” or “left-wing.” I’m sure there’s a more philosophically enriched understanding of these two terms that has them refer to cohesive, dynamic world-views, but I’ll just begin with a provisional, empirical understanding of these terms as signifiers that merely track a difference in priorities in the context of moral foundations theory (wherein left-wing is higher in care & fairness, and right-wing is higher in loyalty & sanctity, and the values of liberty & authority vary independently within each wing), or a difference in cognitive style (wherein the left-wing involves more divergent, “innovative” thinking and the right-wing involves more convergent, adaptive thinking).

That aside, it is definitely tempting to think that fora that moderate only based on form rather than content lead to predominantly right-leaning culture, given that (α) the right-wing has crafted to some success a culture war narrative that substitutes other political debates with a battle over the dissemination of information (framed in terms of free speech v. censorship), and (β) many fora have in fact clamped down on some content creators that are right-wing, pushing their audience to other platforms/fora, and (γ) there has been a popularly observed growth in online left-wing content creators both in number and in terms of audience support following the aforementioned clamp-down.

However, we should look before we jump. There are a few blind jumps in your argument. While ɑ, β and γ are certainly things that have occurred (maybe one could quibble on the details), by themselves they do not imply that the propagation of left-wing ideas depends on β being true. The successful propagation of left-wing ideas and the censorship of right-wing ideas could be two phenomena that actually lack any causal relationship and may not even correlate long-term, or they could be correlated but both be explained by a third variable (or more), i.e. both caused by a third factor (or more). In the former case, where the two phenomena are causally and perhaps even statistically unrelated, consider that historically there have been moments when it is in fact the left-wing that has ridden on free speech concerns. In particular, we see this in the United States circa 1960s with the Free Speech Movement, which was comprised of many activists and students of the New Left with connections to the Civil Rights Movement and the Anti- Vietnam War Movement. If the left-wing can be ascendant while supporting free speech, this at a bare minimum suggests that free speech is not inherently in conflict with left-wing ideas being popular. A corollary of this is that right-wing ideas are not an inherent consequence of an expansive concept of free speech.

Of course, your claim is more specific to internet media and web communications, and it also defines “free speech” in an expansive way that may not have been shared by the 60s FSM (this would require a more detailed exposition of the ideas of the FSM). Maybe it is disingenuous to use the 60’s FSM as a counterexample to the claim that left-wing ideas require speech restrictions based on content in order to thrive. The internet introduces new conditions for speech that lead to quicker higher volume propagation of speech as a default compared to previous telecommunications. Maybe the left-wing was able to promote free speech while having their ideas thrive in the case of the FSM because they were in an academic setting, which gives their ideas popular respectability, and common but popular ideas propagated less widely compared to those emanating from a university setting. That is, academia’s communication with the public was ahead of any average person’s communications with the public at the time, while this disparity has now been flattened by the growth of the internet. Further, one could claim the expansive standard you mentioned for free speech might be crucial to the undermining of left-wing ideas. Any other standards may have varied results.

But, to the contrary, there’s reasons to be skeptical that academic privileges offset what would have been, according to your hypothesis, deleterious effects of free speech on agreement with left-wing ideas. Academia is right now not only more left than the general populace, at least in terms of self-identification and intellectual tastes, but more left than it even was in the 60s which is when the New Left FSM was active. In fact, it is telling that, if the FSM fought for legitimate free speech, there was tremendous political shift in the university system in the long-run after they fought for it (this doesn’t mean there are 0 bias issues in higher education, but that is a different issue from speech restrictions, and again, a leftward bias would have been comparatively less of a case in the 60s then under the assumption that parity in political affiliations in universities is a sign of reduced bias). This also means that, at the time of the FSM, it was entirely possible for left-wing ideas to get significant pushback initially–in fact, if they were fighting for legitimate free speech, left-wing ideas were guaranteed significant pushback, especially initially (there are different opinions of how things have developed since then in regards to campus speech). And yet, both the FSM’s idea of free speech and their New Left politics seemed to succeed. A hypothesis of academic privileges, let alone left-wing academic hegemony, is not enough to explain this–in fact, it can’t, because the growth of left-wing academia is closer to precisely being what followed FSM’s free speech push. Consequently, “flattening” of the communications disparity between university and the average joe is unnecessary to explaining online right-wing resurgence in free speech spaces, as it should have, according to the hypothesis, already been underway with the rise of the FSM (yet wasn’t). This is not to say that contemporary social media has had no effect on the popularity of right-wing content, or that right-wing views have not significantly impacted a portion of the most recent generations. It is only to say that right-wing resurgence from free speech spaces is not explained by the flattening hypothesis, and would seem an anomaly.

As for the notion that your standard of restricting speech based not on content but other considerations is crucial to the success of right-wing views, or the failure of left-wing ones, I should point out that shifts in politeness norms in a culture can follow shifts in social attitudes that correlate with political affiliation, or can follow shifts in social attitudes that reflect movement of the Overton window. These social attitudes are politically informed, but they need not be politically exclusionary. This is because the norms resultant from these attitudes may be followed based on deference to society and the need for social cohesion, without conformity to them at all restricting the ability to articulate ideological commitments that conflict with what those norms seek to protect. Thereby not inherently leading to restriction of speech based on content. Yet because those norms may nonetheless be politically informed, you get high reactance from older age cohorts or older generations, and even more strongly from those of those cohorts/those generations who have right-wing views. This is often connected with an experience of relative deprivation resulting from the new social expectations. This high reactance leads to behaviors that violate or resist those norms, which then leads to those people being publicly shunned. Therefore, it is entirely possible that censorship of right-wingers not be based on their political identification or the content of what they are saying but on correlated speech acts (so, more-so the way they are speaking or what they are doing with their speech) that violate politeness norms, leading to right-wingers being more negatively affected by those new norms. (I think a great example of a norm that fits what I’m talking about is that of using a person’s preferred pronouns or not devaluing someone’s marriage.)

Even in cases where speech may have been restricted based on its political content, if it is occurring on private fora or private platforms, it is likely a matter of those private entities attempting to approach speech restrictions strategically, with public relations in mind. This means, though, that there are other factors which are favoring left-wing ideas in a way that precedes these intra-platform / intra- forum speech restrictions. A shift in the kinds of speech that are restricted may just as well be a consequence of any given set of ideas getting popular or at least hegemonic (inspiring confidence in the more pro- restriction holders of those ideas), rather than an antecedent for the popularity or hegemony of those ideas. Which is to say that those ideas could be perfectly able to succeed in public environments more lax about speech, even if they go on to introduce new speech standards, particularly in private spaces.

Again, at best, I think either you have cause and effect backwards here or you’re missing a third factor or more that can explain the preponderance of right-wing content in fora / platforms with more expansive free speech policy. The idea that the survival of left-wing ideas depends on speech restrictions is a rather questionable explanation for this.