Simple explanation: Russia, more and more, sees itself as one of the last defenders of Western Civilization. Don't forget that the Russian Orthodox Church is Putin's newfound faith. And, while it may see the Greek Orthodox and Roman Catholic (and, by extension, other Christian) brands as mild apostates on some things, view them as overall allies on the more important issues.
Meanwhile, BO sees the Muslim hordes, the illegal alien hordes and the gay mafia hordes as his allies in his quest to destroy and remake Western Civilization in his own image.
To Putin, BO may no longer be a useful idiot. Just an idiot.
Even simpler, if Gay Rights really is a communist plot to bring down a country, then Putin would know that for a fact.