It may be true that the West no longer has a monopoly on gay rights (though the whole idea of 'gay rights' and even 'homosexuality' is - in my view - unquestionably a Western one). But nor does the West have a monopoly on decency and dignity - or even on 'progress'. There may well be ways for sexual minorities to exist quite happily in non-Western cultures without embracing Western sexual identities or politics, including rhetoric about 'rights' and 'equality'.
The problem is that we live in a world where Western cultural and moral assumptions are still spreading globally, even at the moment when Western economic and military power is beginning to be eclipsed. Media and popular culture carry Western assumptions about sex and sexual identity, but Western nations no longer have the power to defend their worldview against reactions. This is doubly unfortunate for sexual minorities in many countries (like Uganda or Russia or Iran) which have existed happily for many centuries, but are now confronted on the one hand with labels and political rhetoric imposed on them from the outside, and on the other hand with a reaction from politicians who perceive them as an insidious foreign influence.
None of this, of course, is in any way to condone what is going on in Chechnya. But it may be that noisy condemnation from Western nations and from gay rights lobby-groups is doing more harm than good. Which raises a question: what do we want to achieve here? Do we want to end this police harassment and improve conditions for men who have sex with men in Chechnya? Or do we want to try to impose our own ideas about sexual morality and identity on another culture?