collision system not affected by physics

I have a character and a wall. They both need to be "static", i.e. not affected by physics, however the character is obviously not supposed to be able to walk through the wall. How do I achieve this?

From what I can find, there's no way around rigid bodies if I want collision, but then both of the objects can't have kinematic rigidbodies because then they are able to move through each other.

Have you considered using a character controller for your player instead of a rigidbody?

It's not effected by physics but can interact with other physic objects and won't pass through rigidbodies (even kinematics).

Note, physics will only be called if you use Move (or AddForce, AddVelocity) and not if you just translate.