I have a room built of cubes (floor and four walls) and I’m using a character controller for my player. There are no rigid bodies involved. When everything is stationary the player collides nicely with the walls. The room is the parent and its children are the walls, floor and the player (which is also a cube at the moment with the aforementioned character controller).
I make the room move through space using it’s transform, and as the player is a child of the ship it moves through space as well. However, after I make the ship go a certain speed, collisions stop working properly and the player will eventually be able to walk through the front and back walls and/or fall through the floor. This usually happens around 80m/s.