Authoritarian communists tend to favor heterosexual relations only.
Sex is very personal for people, and throughout history demagogues have noticed that it’s quite easily to manipulate people by playing on their sexual anxieties. Among these, homophobia is probably to some extent innate – it likely takes a measure of moral reasoning to overcome that innate fear (at least in men).
For this reason, most authoritarian ideologies frown on what the believers see as sexual deviancy. That’s the case whether of Islamic fundamentalists, U.S. Christian supremacists, authoritarian socialists, or mundane things like the Republikan Party in the U.S. or most European nationalist parties.