In our world, the primary act around which the majority of sexual interaction revolves is vaginal intercourse. There are outliers and fetishes and foreplay, of course, but in terms of broad cultural understanding, men and women want - to put it as crudely as possible - penis in vagina.

Now, what if you changed this primary sex act to something else?

This might have a great number of knock-on effects besides just changing men and/or women's preferences. It might affect how the culture views sexuality, it might change the nature of advertising, it might change the standards of beauty, or who reaches the heights of celebrity. Add in biological and cultural quirks and this Alternate Sex Culture could get even stranger.

So let's make one, shall we?

Every Alternate Sex Culture has to have one feature in common. Just one:
1) Vaginal intercourse, while still required for reproduction, is no longer considered the primary "sex" act. It might be considered niche or ignored entirely.

Beyond that, there's a lot of possibilities! Specify your culture with these tags for convenience:

Act: Which act is the new "fucking?" It could be titfucking, it could be oral, it could be footplay, it could be holding hands for Pete's sake. Whatever you decide, that's the new center of the sexual culture now.

Size: How big is this culture? It doesn't have to be the entire world. It could be as small as one home, or as big as a country, or the entire galaxy in a sci-fi context, or an alien planet. Or something weirdly specific, like an aura that surrounds one man or some magical reality-altering artifact. It could even be in a state of flux, a growing movement radically taking over what is normal.

Biological Quirk: A change to male and/or female biology that plays into why this has become the center of sexual culture. Could be increased sensitivity, periodic growth, or even as simple as a natural tattoo that points to the sexual target. (You can add more than one, but for the sake of branch titles there should be one headliner.)

Cultural Quirk: A change to how society works that plays into the new meaning of sex. Alter gender norms, the rituals of courtship, the definition of modesty, public reactions to sex, and so much more. (You can add more than one cultural quirk, but for the sake of branch titles there should be one headliner.)

Your next choice will determine what culture you're going to immerse yourself in, and elaborate further on the specific details. After that, you'll decide the character whose life in this world you'll get to explore. Be creative! Build a world! Think through it thoroughly! And have fun!