The democratic world has been stunned at how Putin has all but outlawed homosexuality while Russian intelligence agencies are going back to typewriters: Putin has brought Terry Gilliam's Brazil to life. Very dieselpunk, no? Kremlin apologists are in an uncomfortable position that would make a contortionist wince in sympathy. Many people have voiced obvious ethical objections to Putin's demonstration of what talk of "protecting children" leads to. Few have paid attention to the politics behind Russia's latest slide into backwardness.
It strengthens Putin's Christian persona and the power of the Orthodoxy, which always been a state tool, in Russian society. The president seems to crave the prestige and power of the USSR while having a system that draws on Tsarism. As Jason Matthews wrote in Red Sparrow, modern Russia "is insecure, wants to be respected, to be feared like the old Soviet Union. They need recognition, and they hate their second-tier status in the superpower stakes. That's why Putin's putting together USSR 2.0, and no one is going to stand in his way.....the second Cold War is all about the resurgent Russian Empire..."
Russian society in any incarnation has usually required a scapegoat. If you're Stalin or the Tsar you cannot run one of the worst states in human history without something to misdirect popular anger away from you. Putin's popularity is decreasing and the economy is so awful that even state media has reported that the RF is set to become the "next Greece." Putin's bond villain stunts (like the world) are not enough he needs a scapegoat.
Normally that role has fallen to Jews, since few if any remain in Russia that is no longer an option. Anti-Semitism has influenced other Russian bigotries; the justification that homosexuals are monsters who prey on children resembles the blood libel. Russian lawmaker Vitaly Milonov said critics of anti-gay laws are "members of the gay lobby" the most fabulous international conspiracy!
Anti-Chechen racism is powerful in most political camps which is deeply influenced by pan-Slavic nationalism, recall Nalavy's call of "Russia for Russians." Its also useless to Putin since it threatens his interests in the Caucasus, anti-Chechen nationalists want completely out of the region hence calls to "stop feeding the Caucasus" which would be disastrous for Putin.
Ethnic nationalism in general is also off limits. He fears stoking separatism and conflict since the two Chechen wars ravaged Russia which is why he promotes phoney prattle about "civic patriotism." He prefers to promote Eurasianism since it has a place for non-Russians and anti-Western chauvinism; an ideal balance for him. The fact that it helps with foreign policy in central Asia certainly doesn't sting.
Therefore homosexuals are an ideal scapegoat. There is no chance that homophobia can inflame conflict, destabilize the Caucasus or harm his interests. Anti-LGBT prejudice is widespread and festering in Russia, exacerbating and rousing hysteria distracts public opinion away from Putin's regime; there is no downside in it for Putin. Bayard Rustin nailed it when he wrote that "the barometer for judging the character of people in regard to human rights is now those who consider themselves Gay, homosexual, Lesbian."