Mytilene/Mytilini is an ancient Greek name for a district and city in Lesbos. It isn't of Turkish origin.

This looks interesting:

https://turkishdailynews.com.tr/article.php?enewsid=97784

I haven't been to Lesbos but Ayvalik is a lovely place. At a guess, Lesviots willing to coordinate with Turks to create an arts festival are not the sort of people who would get steamed up about lesbians. It takes remarkably few bigots to make a whole community look stupid.