I think it might for a little while but not for much longer.
When the influx started, the two oldest and biggest Lemmy instances, the ones maintained by the developers, and thus presumably the flagship instances, were lemmy.ml and lemmygrad.ml. Tankies are definitely overrepresented in those two instances, and since the devs themselves are tankies, there's a lot of moderation bias in favor of red fascist authoritarian regimes even in the nominally "neutral" lemmy.ml — such as them refusing to remove genocide denial or outright genocide justification, while also removing posts critical of China and so on.
You might argue that this doesn't affect you if you just pick a different instance, because the culture of that instance will be different and so will the moderation, but the problem with that is that if the vast majority of users on a network are tankies and are moderated by tankies then that's going to influence your experience of the network as a whole pretty much unavoidably unless you defederate with the largest instances and thereby intentionally hamstring yourself.
So even if you joined another instance, your experience of the site as a whole would be dominated by a tankie leaning culture via comments and posts, and that's where the reputation (deservedly) came from. And it probably did and maybe still does hamper the growth a little bit. It definitely made me, a trans anarchist, think twice about joining.
However, with the more neutral and professionally-run lemmy.world taking over as the second largest and flagship instance, and beehaw as the third (iirc), as well as the overall influx of a variety of users from Reddit, I think over time the dominance of tankies in how the network is experienced by users, even from other instances, will drastically decrease, especially as many instances defederate from lemmmygrad, and so the reputation will also fade.
It matterd because the servers those devs run with their heavy pro authoritarian red fascist moderation and cultural bias were the two largest instances, the flagships, both by virtue of their size and their official nature. That size means they influence users' overall experience of the lemmy network's culture and atmosphere via posts and comments and votes, so yeah, you can sign up for a different instance and that local community won't have that atmosphere and those moderation problems but you're still connected in the network to the tankies and the tankies have the largest and most dominant instances so they have the most effect on the content of the network, and you can't completely avoid them except by deferating and basically hamstringing yourself by separating from the two largest instances.
Thanks to Beehaw and especially lemmy.world though, I think this is rapidly changing and won't be a significant problem for much longer, although there is the remaining concern that the developers' biases will show through in how they develop the underlying lemmy server software. For instance, unlike Mastodon, right now there is no way for you as an individual to block an entire instance, and I foresee it possibly being difficult to convince the lemmy developers to allow that, since one of the hallmarks of Marxist-Leninist ideology is a focus on mass movement building where everyone is forced to interact and join this one giant movement, even with people they don't like or can't get a long with, which could make them hostile to allowing more freedom of association in the fediverse. I'm already seeing tankies from lemmygrad accusing instances that defederate from them of sectarianism and endangering the "movement", in fact.