I know a lot of internet arguments shut down when people start calling someone 'Hitler,' but this unusual Harry Potter story takes that controversial step as its starting point.
Namely, Grindelwald was basically Wizard Hitler.
This sounds pretty extreme, but there's been plenty of internet buzz about this concept since the first Harry Potter book. It starts - as many things do - with:
Dumbledore's Chocolate Frog Card
In first year, Harry and Ron look at Dumbledore's chocolate frog card, which reads:
Considered by many to be the greatest wizard of modern times, Dumbledore is particularly famous for his defeat of the Dark wizard Grindelwald in 1945...
1945 - obviously a fairly major historical date, being the end of World War II - the significance of which was confirmed by J.K. Rowling herself.
In a 2005 interview, Rowling confirmed:
[A fan] asked about Grindelwald. He said, 'Is it coincidence that he died in 1945,' and I said no.
It amuses me to make allusions to things that were happening in the Muggle world, so my feeling would be that while there's a global Muggle war going on, there's also a global wizarding war going on.
This is where we must go back to the hypothesis that Grindelwald is basically Wizard Hitler - the emphasis being on 'basically' or 'approximately.'
There are, undoubtedly, many similarities between the two...
Grindelwald appropriated an ancient symbol for himself
The Nazis stole the manji, a benevolent symbol used in ancient Buddhism, Hinduism and Jainism and used it as the swastika, the symbol of the Third Reich. Grindelwald used the Deathly Hallows - an old folkloric Wizarding sign - as his sigil.
Nurmengard - Nuremberg
Grindelwald used Nurmengard as a prison for people who opposed him, a fearsome structure that bore the slogan 'For the Greater Good' - eerily similar to the Nazi sign 'Arbeit Macht Frei' ('Work Makes One Free' in German) that hung at Auschwitz. Nurmengard is very closely named to Nuremberg, a city used to determine prejudiced laws against Jews and subsequently to try the war criminals that made those very laws.
So, Grindelwald assembled an army, had his own political prisons that his minions were later sentenced to, appropriated and ancient symbol, and the date of his defeat was the same year as the fall of Hitler's regime...
Mind you, Grindelwald is, as far as we know, one of the only Dark Wizards who wasn't totally obsessed with Blood Purity, which is kind of a central tenet of Far Right comparisons...
Besides, it's a theory, an allegory, a collection of influences, rather than a set-in-stone solid fact, so let's treat it as such and have fun with it.