Kinematic rigidbodies

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.

You don't need rigidbodies for this kind of collision, unless you need some kind of physics effect (e.g. bouncing off the wall).

You can add a collider to the wall without any rigidbody. I think they call this a "static collider."

Have you tried using the CharacterController for your character? It is specifically designed to have a collider but no rigidbody. Character Controller