"I feel betrayed that there is a heterossexual quests"
There are no heterosexual quests in the game. You get the 'straight' achievement by simply finishing the game (i.e. battling/saving the King) without leveling up your affinity on any Townspeople or Shopkeepers.
You don't actually have to battle a woman. There are no graphics of unclothed women in the game, so your eyes are safe lol 🤣🤣