You are creating a false dichotomy. Of course it had something to do with Nazism. But it also had a lot to do with the cultural, economic, and political climate of post-WW1 Germany.
Political ideologies are used to motivate or unite people towards a cause or action - not always rational. In that respect they are a tool in the same way as religion is: instill a cause and foment blind obedience.
Now it is YOU creating a strawman.
Nazism by itself is nothing. It is a tool - an ideology created and grown to achieve a certain aim. It is the events of post-ww1 Germany that gave it power amongst the people and led it to assume the proportions that it did and could easily again. You can critisize it - it is certainly evil, like guns can be thought to be evil- but it would have had no power had not certain conditions existed to allow it to grow and become a power. Those conditions are very similar to the conditions that in general tend to lead towards an increase in fundamentalism, extremism, nationalism or ethno-centrism. Christian fundamentalism and Muslim fundamentalism are almost identical in belief. The differences lie in the cultures they are currently living in: secular democratic West - where the rule of law is respected vs. religious, non-democratic East - where the rule of law is situational and corrupt.
Look at Communism - and in particular Stalin. There is nothing explicit in the writings of Karl Marx for example, that legitimized the purges that Stalin conducted. Yet, he managed to use it as a justification for his atrocities. Not to different from the way Christians have misused the Bible, or Muslims have misused their religion.
What is ironic, and the reason I can not take your arguments seriously - is that you use these arguments to maintain a condemnation of Islam - as a whole - yet are utterly blind to the same failings within Christianity - faults that throughout history can be blamed for much war, bloodshed, and murder if one uses your logic.
You then create a strawman by trying to make the entire religion of Islam comparable to the Nazi ideology. It doesn't wash.