I think most species probably align themselves to either the galactic plane or prominent orbital plane of the local star system.
the “up” & “down” directions would be completely arbitrary, though. there’s no reason to think everone would decide on a standard for those.
and species without that certain sense of appropriateness, or an overt dedication to logic, would likely not bother with a standard orientation. and especially when in orbit over a planet, I think everyone would orient their “down” towards the surface.
In more realistic scenarios, “down” is just defined by the direction of thrust. So approaching a ship, they will be down assuming you are decelerating to match their velocity, but they will be up if you are still thrusting towards them.
But all of that has almost nothing to do with how people will think of orientation to other ships since generally speaking you won’t be using eye sight to communicate ship to ship. At that point an agreed upon down will be needed. Probably aligned with galactic or star system to establish a plane, and probably right hand rule to establish up and down. In general given that space is big and ships are small they will just be points on each others radar until they need to dock with each other so it doesn’t really matter how people are actually oriented, as long as when they communicate what they say makes sense to the other side.
edit: or maybe down is towards the currently orbitted gravity well, like towards a planet/moon/star.
Space shuttles would typically orbit with their top side facing towards Earth. Probably because the bottom is completely covered with ceramic tiles.
Could they use “thumb rules” if said species have thumbs? One that us fleshy puny humans use is the right hand rule where a third axis convention (up) corresponds with counterclockwise movement by the hand curl. Of course you could easily use the other hand since they’re arbitrary anyway.
You’ve stumbled across the answer in your own question. The hand choice is arbitrary, and the direction is a binary choice between the galactic plane looking clockwise or counterclockwise. So you’ll get an even mix of upside-down and upside-up ships when you choose that normal direction arbitrarily.
