The source of humour
In my opinion, the Schultz character was a German soldier - but not a Nazi. He had no time for politics or war. He just wanted to get through the war with as little hassle as possible. He didn't hate anyone.
In many ways, I see the Klink character as being similar except that Klink wanted the trappings of the higher rank. If being an SS sycophant helped, fine but only to a point because, to his great frustration, Klink had a conscience.
Both characters were simpletons obviously but both lovable.