Just to be clear, neutral mean's no man's land, not the territory of neutral players.
I've thought about it, the current order is functional.

• own comes first, because most structures are only buildable in your own territory, so it's the default (and if structures can only be built in own territory, it's not really distinctive, hence it's not mentioned in the tooltip then)
• neutral is next, because this is were you build (e.g. centres) to expand your current territory
• enemy is listed afterwards, because such structures are rare (army camp, siege wall)
• allied comes last, because only naval structures are buildable in allied territory, which makes sense: that naval structures can be built on allied shorelines is because otherwise naval maps could be unplayable; that non-naval structures can't be built in allied territory is because building there means directly taking allied land, which is not done

Basically the order is from more to less likely. That it's revered alphabetical is a coincidence.

An argument in favour of listing ally before neutral is that's the order in simulation/components/BuildRestrictions.js, though that could easily be rearranged, if deemed necessary.

I still prefer and order based on owner affinity

Which is exactly why I prefer this order:

• occupy what belongs to you
• occupy what belongs to nobody
• occupy what belongs to your enemy
• occupy what belongs to your ally

while neutral before allied may make sense since neutral here means no-man’s land, I would still put enemy last.

There aren't any structures buildable both in ally and enemy territory, though.

I do wonder, given that there can be neutral players, if we should find an alternative to ‘neutral’ for this use case, and leave ‘neutral’ to refer to territory of neutral players. ‘Unclaimed’, maybe?

The automatically generated tooltips use those precise words:

Therefore I'd strongly recommend sticking with that to avoid unnecessary confusion. If you want to use a different word, then it has to be changed in the relevant JavaScript code files, i.e. beyond the scope of this patch.
Interestingly, the territory of neutral players is considered “enemy” territory. I guess that makes sense, because you don't share anything with them, unlike allies, so their territory is as hostile as that of enemies. Though maybe there ought to be a separate case for the territory of neutral players? I don't know. If desired, again something to change in the JS code, thus outside the scope of this patch.