Moving body with collision but which can't push or pin each other

Godot Version

V4.6.1

Question

I’m not sure if what I’m trying to do is possible. If it is possible I’m not sure how to make it happen.

I am trying to create a specific form of physics interaction. I would like to have a large number of small squares, each of which will have their velocity set to go strait in one of the cardinal directions. I would like the engine to prevent them from clippingthrough each other to the extent possible (i.e. whichever arrives first gets the space). And I would like it so that even when one of their velocity is ramming another into a wall, the second one just continues moving in the direction it’s velocity is set to ignoring any friction from the wall or other square. If two of the squares are in contact and moving in opposing directions, neither of them should move.

Of the two things I mention in the title (can’t push/can’t pin) not pinning each other is the larger priority. The playfield has some static bodies (effectively walls) and I constantly experience an issue where one square is trying to move one direction parallel to a wall and another square moving perpendicular pushes it down into the wall which stops it from moving. The intended experience can survive the pushing but it can’t survive squares not being able to move despite not having an obstacle directly in the direction they are trying to move.

Is there a way to create this effect without writing my own physics engine?