Mixing static and skeletal meshes?

Because it is wholly unnecessary.
The only reason to ever use a skeletal mesh is when things have to deform.
Dealing with cabinets there’s really only one occurrence - cabinets with a blind. Essentially bread boxes. And that’s if you are lazy at doing it in parts.

Re the rest, you are the one asking about mixing baked and non baked.

You cannot bake a skeletal mesh - at least with the base engine.

As such, you cannot “mix” the lighting. As literally everyone told you, in different sauces.

If your cabinet is static and your door is movable they get lit differently when baking.

If your cabinet is movable and your door is movable the lighting is similar but still different from the rest of the scene.

If you enable the force no precomputed light option, everything will look more or less similar since everything will be lit as dynamically as if it were “movable”.

regardless of any of that.
A skeletal mesh will always lite differently than a static mesh. Even in fully dynamic light.