I think what they are referring to is the way reactionaries in some countries (notably the right in Russia and China) consider queerness to be nearly a western invention and queer rights to be some nefarious plot by the west to weaken them. Therefore, one can hope (though it's unclear if this is what would happen) that the US waving fewer rainbow flags abroad would weaken the rhetorical basis for this myth and therefore make things easier for queer movements in Russia, China, etc.