I'm going to get a lot of disappointed visitors for this one.
Three citizens of the Greek island of Lesbos (also spelt Lesvos) are suing a Greek organization named "Homosexual and Lesbian Community of Greece" over the use of the word "Lesbian" in the organization's name. The islanders claim that their geographical demonym ("Lesbian") has been unjustly co-opted by the organization to their detriment. They want the Greek government to prohibit the organization from using the term "Lesbian" in its name.
There is international precedent for the islanders' claim. Terms like champagne, chianti, and Roquefort are restricted by laws in various countries to products originating from specific geographic areas. Apparently the islanders are arguing that the same principles should apply to people from specific geographic areas as well.
Lambrou[, one of the plaintiff islanders,] said the word lesbian has only been linked with gay women in the past few decades. "But we have been Lesbians for thousands of years[.]"
Of course, Lambrou is wrong on both counts - "Lesbian" referring to female homosexuality is attested from 1890, and referring specifically to homosexual females from 1925 - much longer than a "few decades." And "Lesbian" referring to the islanders of Lesbos is attested (in English) from 1601 - nowhere near "thousands of years."
The suit asserts that the confusion arises in English, not in Greek. There are different Greek words for "person from Lesbos" and "homosexual female" in Greek. Incidentally, neither are "lesbian," or even pronounced like it. In Greek, a man from Lesbos is Λέσβιος (pronounced lesvios) and a woman from Lesbos is Λέσβια (pronounced lesvia). The Greek word for a homosexual female is ομοφυλόφιλη (omophilophili) or λεσβιάδα (lesviada).
(In modern Greek, β (beta) is a voiced labiodental fricative, like the English letter v.)
Linguistics aside, the suit is silly and whiny. I don't know Greek law, but under any sane legal system, Plaintiffs would lose.
I'm sure there are other demonyms out there that have developed meanings other than a reference to the people of a specific place, but the only other example I can think of right now is spartan, meaning something or someone characterized by simplicity, frugality, courage, or brevity of speech, through a similar etymological pathway as lesbian. What other demonyms have developed non-demonymous meanings? Post any you can think of in the comments.