Why is Daniel sometimes able to be pushed around / pushed through walls by objects?

[Romulator]

Best guess is the object's body is falling into the character hitbox while the entity is not being interacted with (mass <> 0), which causes the physics engine to freak out with its collision detection and forcibly attempts to separate the two entities by pushing the character body forward and "out" of the entity.

Walls and ceilings in TDD are pretty simple to clip through - they aren't the most solid of static objects, some of which being just planes, and the game is relatively generous with its detection of determining whether Daniel can jump in the case of clipping thorugh a ceiling. With enough force to get the character body more than half way through an object, the physics engine should attempt to separate the player and the object by pushing out.

A better example, in my opinion, than the one you brought up would be the wallclip which is used in Daniel's room (https://youtu.be/HC3cN2o8ZVs?t=306) with aid of a chair. It's positioned in such a way where the chair falls onto Daniel and collides with him that the chair gets into a "stuck state" because of the way the body is constructed with the body including the legs of the chair, and because Daniel is jumping into it. The collision, along with the repeated jumping (which is possible as Daniel is colliding with a wall which allows for multiple jump inputs), he builds up speed to the point where he can clip through the wall.

In your box example, I am anticipating something similar is happening, but to build up enough force, the player crouches, delays input, then stands to collide into the box, and uses the collision force to push themselves through the door.

https://puu.sh/FmN0j/81c5a03645.png

I've fetched the storage box entity and placed it into the Model Editor and these I believe are your relevant settings. Notice it cannot be pushed by player gravity, which may apply to force, but can collide with box the character and notes in the till.