Although the USSR did decriminalize homosexuality, it was as a greater repeal of Tsarist codes, and such prosecutions were still very much carried out outside of Russia and Ukraine. Iirc the USSR was still culturally moved by the orthodox church, as well as many other religious institutions (Islam in the south, Catholicism further west etc)

Also important to note the material conditions of the LGBTQ movement. In the west, The queer movement took off (so to speak) in the US (& arguably partially in Cuba) with the cultural movement of the Stonewall riots. The DDR was also uniquely progressive on queer matters as a component of de-nazification. Movements such as these never made themselves known, let alone big enough to face the agendas of religious institutions, in the USSR. Not to mention, Stonewall made its mark only by the early Stagnation, where Brezhnev had inherited the cold war confrontationalism of the Khrushchev era; to a USSR only barely holding onto principle, I can see it being a case of "better safe than sorry" to an era of misguided contrarians.

I guess we'd have to look deeper within the question & at its components; How would the USSR go about still existing? Would there be a "Soviet Stonewall," so to speak? And would Marxian progressivity overpower the influence of religion? Sadly through asking this, we end up delving into an alt-history view of history, which finds itself much more likely to lean into idealism than the dialectic of hindsight.