Anything can be "inappropriate" if taken in a different context.  Profanity, nudity, racism, etc - appropriate for many in art/comedy (that is kind of the point, to make us think) but maybe innappropiate at work, school, family dinner, etc.

1. The character represents, to some degree, a real-life person responsible for terrible atrocities. Readers in the 60s digesting a comic with a Hitler clone fighting Ben Grimm and Reed Richards, would have had relatives exterminated at the behest of the real Hitler.

2. The hate ray simplifies, or even sweeps under the carpet, a terrifying aspect of Nazi Germany. That genocide occurred at the hands of the bureaucracy of a developed nation. To boil the evils of the Nazi regime down to the rays of a gizmo, potentially undermines the true horror of what happened.

This is tempered by several things.

First, the intent of the story. As several posters here have pointed out, the story (and the use of the character) is well-intentioned. It is a morality tale, intended to point out the evils of the Nazi regime, lest we forget.

Second, it does not seek to portray the real Hitler. It is clearly a fictional tale. No one would get confused and think this attempts to represent the historical Hitler.

Thirdly, I have tried to think of an offensive analogy using a modern day villain like Hitler and have failed to come up with something that genuinely offends my sensibilities. A super-villain based on Bin Laden that tries to bring down skyscrapers by a mind-controlling ray? Possibly, just possibly, there are folks who'd get offended, but I think you'd have to go out of your way to do so, if it was a clone of Bin Laden, who was the villain of the piece.

Those are my two-penneth anyway. 

——

Snarky YouTube commentary probably pales to the protests, hate mail, and death threats Kirby and Simon received from the anti-war activists and Nazi sympathizers.

I really hate that, and not the least of which is because ignoring the Nazis is, in a way, ignoring the Holocaust - and we've had discussion on that topic already.

Once again... who is standing up for the Nazis today? Who is being offended? Outside the White House and some Fox news shows, maybe... :)

*Yes, I saw the Broadway-ish treatment in "Captain America: The First Avenger." I didn't say NO mention. But hardly enough.

Snarky YouTube commentary probably pales to the protests, hate mail, and death threats Kirby and Simon received from the anti-war activists and Nazi sympathizers.

.................

Did this really happen?

Joe Simon here 

"We both read the newspapers," Simon said. "We knew what was going on over in Europe. World events gave us the perfect comic-book villain, Adolf Hitler, with his ranting, goose-stepping and ridiculous moustache. So we decided to create the perfect hero who would be his foil. I did that first sketch of Captain America, and Jack and I did the entire first issue before showing it to (publisher) Martin Goodman at Timely Comics. He loved it immediately.

"But when Captain America came out, America wasn't yet in the war, so the American Nazis weren't happy with what we did to their beloved Fuhrer. ... We had a couple of personal encounters with the Bund (an American Nazi group). But that didn't stop us. If anything, it added fuel to the fire."