Are you questioning whether European countries grant asylum/refuge on the basis of sexuality/gender identity, if those are persecuted in applicant's home country? That is indeed a thing, a quick search away to confirm…
Not just any home country. I'm questioning that this ever happened to some person from Russia (except maybe Chechnya). Even so situation with human rights is bad, it is far from Taliban bad.
Have you searched? I just googled up some stories of LGBT refugees from Russia who gained asylum in Germany.