The SS was not a collection of street toughs, or brawlers like the SA. It was an elite group dedicated to Hitler while the SA were socialistic ex-soldiers devoted to Ernst Rohm. When it came time to deal with Rohm and the SA the SS were the ones who pulled the triggers.
The SS was modeled on the Jesuits in terms of organization and indoctrination. It is interesting that Hitler never wore the black shirt but always the brown uniform of the SA even after the Night of the Long Knives.
What you say about the SA and SS is true -- I didn't know about the Jesuit influence -- but the doctrine was nothing the Jesuits would sign off on. Himmler was an odd duck, and although he insisted that all SS men be "gottglaeubig", vis, "believers in God," it was actually up in the air what god he was talking about. The spooky midnight solemnities at the tomb of Friedrich Barbarossa, the SS-Ahnenerben mumbo-jumbo about Bronze Age Aryans mixed in with medieval chivalry -- men in 13th-century armor decorated with Indo-Aryan swastikas -- made it more than a little doubtful whether he was talking about the God of Abraham.
In practice, Nazism was hostile to real Christianity, even as it battened on Christian virtues and civilization, and if you ever visited europa.com, a neo-Nazi site, you'd see that expressions of waspish hostility toward Christian symbols are common.