One thing I noticed is that many Communist governments are becoming more socially conservative the more they establish themselves.
Be it the USSR from legalizing homosexuality to banning Jazz, Jeans and Jews.
To China, from giving women rights to reviving Confucianism.
Why do regimes with progressive ideologies get rid of them as fast as they implement them?
In communist countries, ideology often takes a backseat to practical concerns. In particular, they seek control above all. Jeans and jazz were American cultural exports, and the Soviet Union did not want it's citizens signing, dressing, and talking like Americans. Jews too were persecuted under Stalin on the fear that they were "Western" or "international" influences on the population, and then again when opposition to "Zionism" became the USSR's foreign policy.
China's softening stance on Confucianism likewise seems to be because it's viewed as a cultural counterbalance to Western influence... but also because its a philosophy that stresses obedience to authority.
After 72 years’ rule, today’s Communist Party is no longer the engine of revolution, but of power retention. Preaching the virtues of a harmonious society and respect for authority now suits it very well. And as Mr Xi pushes Chinese political culture as an alternative to Western democracy, anchoring its ideology to a two-millennia-old tradition is a handy way of conferring legitimacy upon it—particularly as it is, unlike Marxism, a homegrown philosophy. Indeed, Mr Xi calls Confucianism “the cultural soil that nourishes the Chinese people”. It is telling that today China’s all-powerful leader is wont to invoke the thinking of a 2,500-year old philosopher as well as that of Mao.
You didn't mention it, but some observers claim too that China's recent souring on homosexuality is tied to the fear that it's a "Western" influence on the country, and because China shot itself in the foot a bit with the one-child policy and they badly need to increase their birth rate.
At the end of the day though it's worth remembering that nearly all Communist countries were deeply conservative countries before Communism. There were practical reasons anti-Semitism reared its head again in the Soviet Union, yes, but you can't discount the fact that a lot of its leaders just never abandoned the beliefs they picked up in Tsarist Russia.
As practically all self-declared communism-seeking regimes turned out authoritarian, they had less need for internal 'Permanent Revolution' and more need to stamp out destabilizing 'deviationism' (i.e. not agreeing with the supreme leader). Once you have an extensive repressive apparatus in place, it's easy to use it for whatever.
Also, most of these regimes exhibited an increased degree of nationalism over time --true, in part due to wars not always started by themselves, but anyhow these created the need to genuinely appeal to a broader domestic base (despite the lack of true elections, self-motivated bullet catchers were still needed). And since the regimes were repressive in mindset, genuinely appealing to those with a repressive worldview in other matters was a relatively easy social contract. And so was the use of internal scapegoats of all kinds. Even better when they can be easily painted as a 5th column of an external enemy. It should be said here that this scapegoating mechanism also works fairly well in 'illiberal democracies'.
One thing to note is that revolutionary regimes have often tried a large variety of cockamamie schemes that shortly had to be scrapped.
Mao's backyard furnaces are a prime example of this, since revolutionary regimes often inherit an undeveloped culture and economy, and existing technical experts who could potentially better control policy errors may also be amongst the political opponents of the regime who have to be purged (because the technical experts may be relatively privileged under the old regime, and whose rentier behaviours may be causing its overall backwardness).
In the early stages of the Soviet project, many reforms based on sex equality in the workplace had to be dialled back somewhat, because it upset sexual relationships and caused crisis in reproduction. Instead, the Soviets learned to organise work around motherhood. This was only shortly before they had to spend millions of soldiers' lives fighting off the Nazis.
There were also experiments with 6-day (instead of 7-day) weeks and the abolition of the common weekend and traditional Sunday day of rest. The rationale was to improve the employment of plant and capital machinery, and therefore industrial capacity and labour productivity. But this too was abolished when it made it impossible for couples, families, and friend networks to socialise together properly.
In terms of Soviet anti-semitism, this is often hyped by bourgeois Jews and Jewish identarians who were expropriated from property, whose religious practices were stifled (likewise with Christians), and who often fled to the West with a strong mentality of grievance (much like Cuban exiles, for example). There was also paranoia later in the Stalinist era that those who maintained Jewish identity, or who might be suspected to have such an identity, could be part of an enemy sympathy network.
But in fact, those who were merely Jewish by heritage but were clearly loyal to the Soviet project, were able to do very well. Unlike for example under Hitler, where people deemed Jews were slaughtered on heritage grounds regardless of their politics, sympathies, or genuine self-identity.
So the ultimate answer is simply that regimes learn that many innovations in culture or social organisation do not in fact work properly, and they then reverse or re-adapt the changes.
It would be a mistake to characterise the USSR as "socially conservative" though - in any given year of its existence, it was considerably more enlightened on many social issues than the capitalist West.
All your examples are authoritarian states (and your observations are common across economic systems among such governments)
So your actual question isn't "why do communist countries [...]" but rather "why do authoritarian countries trend towrads social conservatism".
And the answer to that is quite simple:
Progressive movements are the most likely place to start a revolution or protests (Edit: in a conservative government, which most dictatorships are as they are trying to preserve the status quo).
So in order to maintain the current power structure you do not want progress in any way (as some social progress would encourage asking for more and eventually the people would ask for participation).
Furthermore, as evidenced by the USA, by intentionally keeping the societyl squabble concerning rather inconsequential (for the system, not the people) topics like abortion, homosexuality, etc. you keep the progressive forces in the country too busy to question the system overall and you have room for compromises when conflict emerges.
And in order to put more distance between the "current progressive fight" and your power structures, conservative pushback makes sense and gives you more room to compromise to calm outbreaks of protests etc.
For anyone vaguely familiar with social science research in this area, it maybe shouldn't be surprising to often see such a pattern of ideological shift in real world examples, from revolution to post-revolution. It's not necessarily difficult to argue that those seeking change and improvements, reform and revolution might tend to be those who are more radical, socially liberal, and progressive. Presumably in most cases, the early revolutionary activists, organizers, and leaders would disproportionately, though not entirely, fit such a description. But I'm open to counter-arguments.
To my mind at least, this seems to be common sense. And one could argue that it's confirmed by the research on the relationship between ideology and personality. It can be understood through the strong and well-established correlations of liberalism, openness to experience, fluid intelligence, original problem solving, intellectual curiosity, exploratory behavior, adventurousness, perspective shifting, pattern recognition, tolerance for cognitive dissonance, cognitive empathy, compassion, (uncertainty and ambiguity), cognitive complexity, cognitive empathy, etc (Xiaowen Xu, et al, Beyond Openness to Experience and Conscientiousness: Testing links between lower-level personality traits and American political orientation).
These are generally what people think of as social liberalism and liberal-mindedness, even among people who don't identify as 'liberal'. The key component would be the personality trait 'openness to experience' (i.e., being fine with the new and different), as constrasted to 'conscientiousness' that's linked to conservatism. As William F. Buckley put it more prosaically and famously, “A conservative is someone who stands athwart history, yelling Stop, at a time when no one is inclined to do so, or to have much patience with those who so urge it.” To put it in context, there is a reason conservatives aren't prone to revolution, although they'll occasionally join a revolution and co-opt it; such as explained by Peter Turchin's theory about how surplus elites become counter-elites and cause intra-elite competition (End Times). That complicates matters a bit.
As for an extreme example of 'openness', consider that white liberals are the first US demographic to measure high on a pro-outgroup bias, as discussed by Zachary Goldberg (The American White Savior Complex; & Explaining Shifts in White Racial Liberalism: The Role of Collective Moral Emotions and Media Effects). That is to say that fewer of them identify with an exclusive and exclusionary social identity of being 'white', 'liberal', or 'American'. Quite the opposite, they specifically and most strongly uphold the rights and value of those typically deemed as outsiders within the thought of both conservatives and the establishment, which is what defines their ideological identity.
As the leading voice of the American Revolution, Thomas Paine would be a case in point (the first woke liberal and SJW?), when he not only claimed to be a "citizen of the world" but actively sought to spread revolution around the world, along with seeking to promote the rights of women and blacks. Whereas those who gained power in the new United States were without a doubt far more conservative and, in some instances, violently suppressed further revolt. For example, President George Washington, as a counter-elite treated as second class aristocracy, joined the American Revolution only to later put down the Whiskey Rebellion. As a result of reactionary backlash, after the US Constitution was established, fewer Americans had the right to vote than under the British Empire; not to mention revolutionary suffragism and abolitionism were quashed. A conservative mood took over for some generations before social unrest broke out again preceding the American Civil War.
So, for those who don't share the above liberal-minded traits, they'd more likely have been satisfied under the previous status quo and would more likely fear instability and disorder, in that they'd unlikely join a revolution or only do so under reluctance. And those same kinds of people who want to maintain order over all else will be those most motivated to seize power and re-establish order again, either during the revolution or after it is over. That would match the well-established link between right-wing authoritarianism, social conservatism, group conformity, conventionalism, and fundamentalism; all negatively correlated to 'openness'. It also fits in with those high in social dominance orientation seeking power and, when lacking, seeking to create high inequality. The leveling of revolutions tend to be reversed over time, and eventually the pattern repeats (Walter Scheidel, The Great Leveler).
From the Russian Revolution to the Soviet Union, this was seen with the radical Bolshevism replaced by socially liberal Leninism that in turn was replaced by socially conservative Stalinism. Roger Pethybridge has written about this in his academic writings: Stalinism as Social Conservatism?, The Social Prelude to Stalinism, and A History of Postwar Russia. And as noted, a similar pattern was seen with the American Revolution. I'm not sure there has ever been a thorough study to see that the same observations can be made in all or most cases, but it would be harder to imagine the opposite pattern where a conservative revolution that led to a liberal society. If such an example exists, it would make for an intriguing case study, as it would appear to be extremely unusual.
Revolutionary regimes often face practical challenges that force them to adopt more practical policies, these policies are often more conservative. Economic hardships, geopolitical pressures, and internal conflicts can push these regimes to prioritize order and discipline over ideological aspirations.
