There is a federation standard for which way is "up" based on the plane of the galaxy.
So at least that explains why Federation ships always meet on "level ground"
as for why the romulans, klingon, and various other non federation, especially non friendly species from the other quadrants, would be oriented the same way?
Idk, maybe the progenitor race from that one single episode of tng that never showed up or was spoken of again made some kind of subliminal or genetic memories of which way up should be.
Somewhere, in Alpha Centauri, in the bottom of a locked filing cabinet stuck in a disused lavatory with a sign on the door saying Beware of Leopard, there is a very important looking document titled "This Side Up".
Do both sets of progenitors look the same, act the same, have the same background or goals? Or did they take a vague story and write their own version with their own appearance, their own background and goals?
The galaxy is about 100 times wider than it is tall, so if i am bump into someone while we are both crossing a sector, we will likely be on a similar plane, even if we are likely at wildley different "eleveations" . On top of that, being close enough to a ship to make visual contact with a really good telescope (say 20,000km) requires a conscious effort when talking about galactic scales.