to me it's as simple as this
i want to play soccer, maybe play coed league instead of men's.
i like art, maybe take a class instead of just do it alone at home.
i'd like to learn to surf, maybe take a class instead of hire a personal lesson.
you're not being fake, you're pursuing your interests. pursuing interests can improve confidence which translates to dealing with people. and you meet people with those interests in common.
if you're religious, lots of churches have singles groups.
it also wouldn't hurt if you balanced out hanging with the guys who want to drink beers and watch sports together, with hanging with the friends who socialize and have female single friends.