TL; DR: Anti-socialism among anti-socialist Christians seems to really be about #authoritarianism (about 500 words)
A lot of #Christian groups (arguably all of them, if you go back to Acts chapters 2-4) have a history of socialism or communism or collectivism. The most prominent modern American sects have become rabidly anti-socialist since the mid-20th century. My former group, the #LDS church, actively practiced and even preached as mandatory doctrine a version of #communism for most of a century.
The anti-socialist Christian sects have various ways of explaining away the 180 they pulled on #collectivism, whether that took a few decades or a few centuries. The Mormons tend, in my experience, to say it is God's ultimate plan, but humans are dumb and selfish and not ready, yet, so they fucked it up (never mind that this rationale relies on an Authorized LDS History in which the "United Order" only lasted for a few years in the mid-1800s when, in reality, it persisted in many areas for decades longer).
Whatever the other justifications, Mormons will eventually arrive at, "Unlike heathen imitations, our system was good because God was in charge." Of course this actually means a small number of God's appointed men were in charge, though Mormons will not usually see an important distinction between these two concepts.
The explanation of why Mormons no longer practice #socialism (at that scale, anyway) never includes the idea that putting a few men in charge of the material welfare of a much larger group of people might be a problem. No, it's always "people are too selfish", implying it's the governed who are responsible for the system's failure, not the governors or the system's structure.
Opposition to "communism" and "socialism" in LDS (and, AFAIK, evangelical) groups during the Cold War relied heavily on standard American anticommunist images of bread lines, political purges, gulags, political prisoners, stifled free speech, propaganda press, crushed dissent, etc. It took me a long time to start seeing this as a shell game: Socialism is bad because lack of freedom. Evidence: economic catastrophes, restriction of rights, abuses of citizens, which seem more about authoritarianism or totalitarianism than socialist principles. Nope, it's socialist principles that are the problem. Many people have noticed that the loudest followers of the Guy Who Said We Should All Share seem to also be saying that sharing is evil.
Side note: it goes without saying you should never, ever suggest that an authoritarian religion also relies on restriction of freedom, unless you want to become persona non grata in your own community. I currently believe that a lot of the apparent insanity we see on the American religious right is driven by hyperlocal concerns about friendship, community, fitting in, etc.
Back to the main argument: I suspect any observations about authoritarianism in Christian socialist/communist history are aggressively discouraged within anti-socialist Christian churches because those churches still rely on centralized authoritarian systems for their existence. Freedom is all well and good, but too much freedom (defined by the people in charge) would be *gasp* #anarchy.