The Queer liberation movement has long been spearheaded by communists. Harry Hay, Sylvia Rivera, Rudolf Klimmer, and many others, were all communists who, in some form or another pushed forward the cause of queer liberation.
On the whole, Socialist states in the 20th century were no better or worse on queer issues than any liberal democracy. We were treated like shit pretty much everywhere. They were not special in this regard.
A notable exception was East Germany, which, though not without flaws, had a far better queer rights track record than its Western capitalist counterpart:
The HIB (Homosexuelle Interessengemeinschaft Berlin) was established in 1973 with the belief that ‘homosexual emancipation is part of the success of socialism’.
Modern ML states like Cuba have made immense strides in queer rights in the modern day, and progress in, for instance, China is slow but steady.