That which is affixed to the wall would be considered real property and stay with the house. The cabinets, even though you paid for them, are attached and nailed to the structure.
I have seen owners remove washer/dryers and draperies. Only in very rare....almost bizarre circumstances, have I seen an owner remove cabinetry. Such activity might be constued as vandalism.
I am not an attorney and this is not legal advice.