A state must have a territory. A government can only govern when there is a region over which it governs.
A nation can hope to form a state only when that nation occupies a defined territory. Right-wingers, LGBTQ people don't have a territorial home.
Consider the "nation of redheads". There are red-headed people through the UK. How could they exist a separate political entity to the non-redheads. If I am engaged in any kind of interaction with a red-head, then what laws apply? mine or the redhead laws?
A state with territory can function. If you are in the UK, you have to obey the law of the UK.
And redheads are at least fairly identifiable... but what if a redheadded man loses his hair... or dyes it. If it would be unworkable to have a red-head state co-existing, it would far far worse to have a "left-wing" state and a "right-wing" state occupying the same territory.
So in practical terms this is a non-starter. Unless a group has a reasonably clearly defined territory, it cannot become a State.
A historical example of this is the state of Israel. For thousands of years the Jewish nation existed within European societies. There was no possibility of European Jews becoming a state, as there was no territory held by the Jewish nation. It was only with the designation of a territory in Palestine as a Jewish homeland, was it possible for a Jewish State to develop.