There is a good song, https://www.youtube.com/watch?v=yMmEt1sL7GU , "Ours and theirs", by Alexey Ivaschenko and Georgiy Vasiliev, which lists a bunch of differences - which, of course, exist even between pretty close cultures - and, characteristically for authors, concludes with "there are many things which you can't divide on ours and theirs".

It's like talking about ideological divide between USSR and USA - even back in late 1980s it was proclaimed loudly, but nobody came out defending USSR in late 1991. Gay relationships are nothing new in Russia, and official condemnation doesn't mean it runs deeply against cultural grain.

Don't forget - Russian people and Russian government are strongly opposing entities. On the other hand, Russian expats in USA have comparatively little problem adjusting to American culture. Standards are indeed very similar - more so than, for example, in comparison with some Asian or Middle East cultires.

To be fair, much of America responds in a negative way to that already

To be fair, when the Supreme Court handed down the Obergefell decision to grant freedom for same sex marriage, there wasn't an uprising or even a protest that drew any attention. It's an issue that has been accepted by the public at large, even the religious crowd at large.