You're not the only one with German ancestors [or to ask how it was allowed to happen] the only difference is, my German ancestors left in the 1600 and 1700s.
But I don't know if you were ever called a nazi as a child by classmates because you were born there because your father was in the Armed forces... Funnily, the biggest one for doing that to me looked a lot like a ginger Adolf.... especially with that stupid matching comb across his lip.
Post war America was very eager and willing to get a hold an all kind of Nazi scientists, their research and knowledge and even imported them if they saw it fit like
Wernher von Braun, who became famous with NASA but before developed the rockets V1 and V2, which where fired at London during WWII.
America was also not above of getting a hold on all kinds of torture manuals and inhuman research results being conducted within KZs, like done by Dr.
Sigmund Rascher in Dachau who by any means was a mass murderer.
And in hindsight some people like Max Hastings have a hardon for the efficiency of the Wehrmacht compared to the US Army back then in WWII, being published 1985 in the Washington Post ("The inescapable truth is that Hitler's Wehrmacht was the outstanding fighting force of World War II, one of the greatest in history.").
Well we are living in interesting times nowadays; as a result of the American reeducation and denazification after WWII and having begun and lost two world wrars during the same decade with only 25 years time begin their beginnings, and the latter having really devastated the whole country German militarism is quite dead. Having an army is more considered as a strained burden and painful necessity, but since the unification even the need for an army was being disputed quite much. We are not proud on having an army, the founding of the Bundeswehr in 1955 only ten years after WWII end was more or less a scandal.
This is quite different to the very much war centric behaviour during the 19th century, especially done by Prussia, where war was just being considered as a continuation of politics by just other means. WWI changed that point of a view a lot due to the population suddenly somewhat being involved having not much to eat, WWII then really buried it at the grave yard.
If Germany would start to rearm itself again and rebuild and increase its army at large not just for the means of defense, but to be used globally, this would lead to heavy inner European tensions. Especially Poland would not be very amused about it, but also the UK and France probably would suddenly remember quite painfully what could happen when Germany becomes war centric and embracing it.
So far Germany is embedded into NATO, and this was one of the moves to prevent such a scenario as lesson of WWII. The irony of the history though is that we've now got President Trump, who demands the increase of the military budget up to 2% of the GDP, at best yesterday. We on ourselves are not so very keen about it, but raising it somewhat reluctantly at the moment.
Having a GDP of 3.744 trillion US$ per year means that we would increase - if we would abide Trump's wishes over night - our military budget from 49.5 billion US$ in 2018, which is 1.2% of the GDP, to 75 billion US$, which would become the 3rd biggest miltary budget globally after the USA and PRC, before Russia with 61.4 billion US$, France with 63.8 billion US$ and the UK with 50 billion US$.
For sure our neighbors would love to see that happen... it would be a nightmare for them. Germany also has tons of really interesting nuclear waste products still being stored in La Hague, France and Sellafield, UK. Over 60 tons of Plutonium are being stored there, which it has to take back some day because it won't be allowed to be stored there forever, and nuclear power plants are still in operation - in short if it wanted to have some own nuclear nukes, Germany has the materials readily stockpiled and also the knowledge and access to technology to do so. It just is better for the national security to not have any own nukes - again due to history. So instead it has access to American nukes, which are being mounted on German fighting planes in Büchel, but only can depart if the American government approves the start.
In short: every country has its own dark moments, we are quite aware of our own. And due our history in the 20th century our love for playing war just vanished out of the windows, and has been gone since still until today. This is why many Germans themselves do view the demanded increase by Trump of our military budget very, very critically and disapprove it.
Yet again despite all that the extreme right is on the rise again in Germany. The new Nazis are already in all of our parliaments and their share has been increasing over the years, because many people are fed up with Merkel and it's like in most other countries as well - if people do feel like they might lose something, they are movnig to the far right nowadays, not the left. Poverty is increasing like mad, rents are going through the roof and our infrastructure is decaying like mad due to the wonders of austerity. This flocking around the right was true in 1933, and is true again.
The reason why is simple - most poor are disillusioned and don't vote at all, but they are the reservoir which the left would need to appeal to but the left tends to ignore because they despise them as unworthy and human trash. Instead the left are trying to appeal to the middle class, which in return views the left as devil incarnate, so as a result the disullisioned and frightened middle class which fears its descent is voting for the extreme right like mad which in reality most of the time acts like a catalyst to the descent, not a brake. That's true in Germany, UK, America - and many other countries at the moment as well.