I suspect the fundamental culture would be nothing radically different from the national culture(s) from which the inhabitants come. Still it might feature certain Aspie-friendly adjustments such as literal communication (no saying one thing and meaning another), and would likely be more erudite especially with encouragement of people's special interests, something that the culture would hold dear to. You'd still have an element of more NT-like culture and interests there, as some inhabitants would be more NT-like than others, but with more skewing towards an erudite/special interests culture.
The culture would be classified as being very secular - because even if there are some religious Aspies around, diverse existential points of view would mean it could be nothing but secular. Also because ethnic, racial, religious and other prejudices would be stamped out and considered shameful, even more than in a contemporary developed, progressive nation. And it would be classified as very individualistic - for quite obvious reasons given Aspies' interaction style. People would form groups and communities like anywhere else, of course, but there'd be more discouragement of peer pressure and pressure to conform. There'd be great social responsibility when many inhabitants have such high needs due to how their autism affects them. Thriving sub-cultures would be found within the nation, due to individualism and special interests.
That's an idealistic view anyway. I suspect it's more likely it wouldn't quite be the Aspie utopia I tried to describe above. Realistically, big trouble would be ahead demographically and socially, what if we are to go with the supposed figure of 4 males with an ASC to every female. So initially there'd be sharp drops in the population with consequent social problems as at least 75% of the male population would die out without having reproduced before anything like an equilibrium is reached in the sex ratio. That's just assuming natural passage of time and life span, because a more significant social problem would be simply the competition for females. Every man (especially with the majority so sexually frustrated) for himself, it wouldn't be pretty, and not exactly a safe haven for the more vulnerable, meek or shy Aspies. It would be the bolder and more alpha male like Aspies who'd prevail, maybe by exploitative, maybe even by violent, militaristic means, especially as their boldness gives them more chance of successful interaction and reproduction with females anyway. Even if the population are all Aspies, the bold and strong would exploit the shy and weak, in fact the sexual imbalance would far outweigh advantages of the Aspie culture.
Better for an Aspie culture to have a distinct niche within contemporary society, than to be independent.
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The greatest kingdom in all the world. All hail Lilliput!