Aren't people from Lesbos called Lebosians? Completely different thing. Anyway, they should have done this earlier, but now it's ingrained in the vernacular, so they're probably stuck. I could think of worse things to be called. They should just go with it and have some annual celebrations or something. That would increase tourism if that's what they're aiming for.
No, it's not a completely different thing. The poet Sappho was from Lesbos. She was called "the Lesbian" (with a feminine ending) because she was from Lesbos. She was also bisexual (at least, she used a bisexual persona in her poems). In the ancient world, the feminine form of the adjective for a person from Lesbos, when used as a substantive (i.e., a noun), came to be used as a euphemism for a homosexual woman (yes, even though Sappho herself, or at least the persona she projected in her poems, was bisexual, and not exclusively homosexual). In 19th century England, this euphemism came to be used as the normal word for female homosexuality.
In Modern Greek, the name of the island is pronounced "Lesvos" and spelled "Lesbos," so one could distinguish between the two uses by referring to the people as "Lesvian" or "Lesvosian" (or "Lesbosian" or "Mytilinean," after the capital city of the island, the name of which is also sometimes used as the name of the whole island).
Think of it this way: how does an English-speaker refer to a resident of Frankfurt? Of Hamburg? That does not mean that the cuisine of Frankfurt is well-represented by the frankfurter, or the cuisine of Hamburg is well-represented by the hamburger. Metaphors sometimes cause the associations of the tenor to become attached to the vehicle. It sucks to be them, but that's not going to change.