Anonymous They both sound okay but is one better than the other. Difficult choice. Grammatically, they're both fine.
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AnonymousThey both sound okay but is one better than the other.Difficult choice. Grammatically, they're both fine. In your place I wouldn't worry about the exact order of the adjectives. Use whatever sounds better to you in the context you have in mind. I think I'd write "American gay men", but I wouldn't insist on that order.
AnonymousGay American men or American gay menI would say that the former contrasts more with straight American men, and the latter contrasts more with gay men of some other nationality. This may influence the choice in certain contexts.