This is no coincidence. The SS as an organization did indeed resemble the Witnesses. I found that out as I read a biography of Himmler. The SS under Himmler had a rational-like kind of fanaticism. They did not shout "fanatic" from miles away like the SA battalions; they were instructed to live an exemplary family life, and seem serious and sober (they were heavy drinkers in secret), but that didn't make them less fanatical. Instead, their rationalization made them the most dangerous of all fanaticals, because they coldly rationalized every despicable thing they did.
Himmler often wrote letters to the Body of Generals" so to speak, and sometimes to lower officers, to give answers to questions they asked, and usually gave unnecessarily specific guidance in various tiny details. That surely reminded me of BOE letters. Plus, Himmler was in fact familiar with jws and expressed admiration for them. In his own words (taken from Longerich, Himmler, 2012):
He came to respect the Jehovah’s Witnesses, tens of thousands of whom
were imprisoned in his concentration camps as a result of their pacifist and
anti-Nazi attitudes, because of their stubborn will to resist: ‘If their fanaticism
could be harnessed for Germany or a similar fanaticism be created in
the nation as a whole in wartime, we would be stronger than we are
today!’ They also lived frugal lives and were hard-working and honest.
For that reason he not only employed them in his own household and in
those of friends and SS families, but expressed the view that precisely these
qualities should be propagated among the suppressed nations in the east,
where in addition the Jehovah’s Witnesses’ pacifism was extremely welcome
to the Germans! In July 1944, in a long letter, Himmler therefore
ordered the then-head of the Reich Security Main Office, Dr Ernst Kaltenbrunner,
to export the religion to the occupied eastern territories (which by
this time were no longer occupied): ‘In the case of all Turkish peoples the
Buddhist faith is suitable but for other nations the teachings of the Bible
Students [ Jehovah’s Witnesses] are the appropriate ones.’
Btw, notice the irony of the Nazis welcoming the jws pacifism in the occupied countries, convenient as it was.