Renai Flag Zero Joshi no Meisou

Tooni Himeki, who grew up playing otome games, moves to an island populated by only beautiful men, & every guy she takes an interest in is gay, & she is NOT a fujoshi. But that won't stop her plans to create an all boy harem. & the very first guy she sets her sites on becomes her biggest rival & sort-of friend.

(Source: MangaUpdates)