Does the mesh have an LOD?
Otherwise, I think the easiest way would be to make the door its own static mesh with its own material.
The only way to avoid that is to make sure they’re further apart or to not have a wall behind the door.
What happens is that there’s a limited depth range for the camera and when you get further away it stretches that out across a longer distance which can mean that surfaces that previously were on different depth levels end up at the same depth level and then you get that effect which is called Z-fighting.
Thanks for the tips guys! I guess I’ll use a different model. =)