So you don't actually believe that "their values alone" rhetoric and all statements to the contrary are hypocrisy. Got it.
What's bad about that? Particularly what's worse about that than a "NATO psyop?"
It's worse in that it's not just L.G.B.T. organizations but all organized movements across the spectrum. I.e. I am not opposed to those orgs by virtue of their agenda, but by virtue of their foreign provenance.
In the information age, the era of mass communication, you cannot seriously begrudge the borrowing of iconography. Especially something as little as an acronym and a flag, both of which came from grassroots movements anyway.