I know it’s a joke but it really should be the other way around

Sappho is the OG, and modern gay women are just cosplaying as Lesbians

If she’s not from Lesbos then it’s just sparkling dyke

Yes, non-lesbian Lesbians (proper noun) sometimes begrudge tourists taking their demonym. The lesbian community online tries to be generally inclusive, (with smaller gatekeepy sects) so there is a conflict.

Still, Lesbians do like lesbian tourism money, if not always the tourists, themselves.