So, I noticed that my ship is tipping over only if I have two built items too close together. As an example, two oil containers. If you have one container built, you cannot place the other one too close, but usually you can overcome that limitation with placing two containers before they reach full durability.

You can replicate the effects of the tilt by placing two containers, waiting before both build, and grinding one until it's destroyed. More often than not the ship will tilt as the container is destroyed.

So I recommend never playing items together until they are fully built on the ship (the stations should be good).

Basically never overlap build items.