First, Elon Musk gives the Nazi salute at the Trump inauguration ceremony.

Then the ADL attempts to say that this was not a Nazi salute.

This is utter gaslighting. ADL has spent most of its history gathering intelligence on antisemitism, calling it out publicly, and working with government to wipe it out. ADL has identified the “awkward gesture” in high school students, militia members, and prison gangs and has designated it as a Nazi salute. Musk is evidently too rich and powerful to be called to account.
Musk’s vocal support of AfD, the German hard-right “neo-Nazi” party, of course, has no bearing on interpreting the “awkward gesture.”
My guess is that Musk’s damage control PR team drafted the entire post and handed it to the ADL for unaltered reproduction.
It also appears that I have inadvertently been contributing to a phishing operation that has been illicitly using the ADL logo since 2014. I may have to contact the FTC… Wait, never mind.