Let's not invent things about the Orthodox church. Yes, a lot of Russians self-identify as Orthodox these days - but most of them rarely so much as see a priest, still less listen to what one says. Russian "religiosity" is, mostly, of rather mystical new-agey type - they'd pretty much believe in anything that appears to be a religion. Tradition is, mostly, followed in its breach. Though, of course, the STATE, such as it is, is getting increasingly identified with the Russian Orthodox Church. And the Church is actively using this identification to attack all sort of competition that has emerged.
Yes, it's true. An overwhelming majority of Russians are Orthodox Christians now - but in name only.
Anyway, no need to invent anything new. Russia has always been homophobic and illiberal. Under communism, male homosexuality (literally, "men lying with men", in the language of the Communist criminal code) was punishable with prison. At least, we are still not there - man lying with man by itself is not (yet?) punishable in the new Russia.
Homosexuality was illegal and usually punishable in the USA and many Western European and Latin American countries until 60s-70s, but things have changed dramatically in merely few decades. The interesting thing is that Russia, unlike others, still stays in the homophobic past.