Lets answer these questions between us and get the basic world building down. I'll start.
Why were we all separated onto different islands?
An evil homophobic dictator took over the entire world - Hitler-style - and separated the entire population into three categories. That's how the world became as it is, but now with a hint of resistance below the surface like every good dystopian.
Did the government sanction this? If so, why?
Why didn't we revolt against this tyrannical government?
Where are these islands? How were they chosen?
Are the continents of the world abandoned?
What kind of resources are on each island? Are they the same or different?
Does each island have a right to form its own government or does the government that segregated us still rule?
If so, what island do they rule from and how do they communicate with the other two islands? If they can communicate with the other two islands, can all three islands communicate with each other?
If the straight people keep reproducing, won't their island become overpopulated and their resources depleted? Islands only have so much space right? Do straight people stop having gay kids? Isn't it a fact that, to date, straight people are the largest manufacturers of gay kids? If a gay kid is born on straight island, do they get sent to their appropriate island? Wouldn't that aid in the re-population of gay and lesbian island?
What about people who are attracted to more than one gender? Are they just lost at sea, floating aimlessly? Is the ocean full of listless pansexuals, floating nowhere? Or are they trapped in some sort of purgatory because they don't fit on any one island?
Are there trees on lesbian island? Is it conceivable that if there were, a large group of lesbians could build a boat? Have you ever seen lesbians around timber? If they built a boat, could they travel to gay island?
How far apart are the islands? If they could travel to gay island, would they be able to collect semen, return to lesbian island, and repopulate the island? Would they be able to send some of those children to gay island?
Do trans people exist in this world? If so, wouldn't they be able to aid in repopulation?
If the lesbians decided to declare war on the heterosexuals, would they be able to reach their island? On the way to heterosexual island, could the lesbians pick up the gays and scoop the floating bisexuals from the sea? If so, would they all be able to go and attack heterosexual island together, wiping out its people's, stealing its children and taking all its resources?
By the way, I wholly want us to include this part of the post:
I am so here for an asexual sky nation. We live in floating cities and master the wind currents. Newly minted ace youths are sent up to us in baskets suspended under hot air balloons. We breed giant birds to bear us through the skies, or else build ourselves wings and gliders to fly in their midst. The only land we know are the tallest mountain peaks and the world is a bright blue gem spreading out beneath us.