As stupid as I think lefties are for trying to claim the fandom as a whole by gatekeeping it based on sexual identity, I believe there's a better, more valid argument to be made when it comes to excluding communists from furry communities.
The furry fandom functions in a strongly anarcho-capitalist manner because it operates through decentralized, voluntary exchanges in which creators trade their labor in the form of art, fursuits and other goods or services for money, while participants form voluntary private communities.
Communism rejects private property, monetary exchange, and the non-aggression principle in favor of collective control.
As a result, communism is incompatible with these values and principles, so individuals and private groups within the fandom have every right and incentive to withhold association from those who advocate for it or identify as communists.