The problem with comparing Islam with Nazism

Of late, I have seen (what I regard as) a problematic tendency among some atheists to equate Islam with Nazism. Their point, as I gather, is this — What is the difference, when both are totalitarian ideologies that are hostile to the out-group (in the case of Nazism, Jews and other non-Nazis who are against racial supremacy, and in the case of Islam, the disbelievers)? Both ideologies are in a sense reactionary and based on perceived grievances (Aryan race vs Semites, monotheists vs polytheists, those who distorted monotheism and atheists). But there is a big difference between Islam and Nazism.

The first, really, is that it is a category error to compare the two. One is a purely political ideology based on racial superiority, and the other is a belief system borne out of cultural practices, history and the human need to find greater meaning in life.

There was a discussion on this issue on Facebook. The question really was, can we separate “ordinary Nazis” from Nazism the way we can separate Muslims as people from Islam the religion? Here’s how I responded:

Nazism is purely a political ideology with race superiority as a significant founding principle. Islam is a religion — which means a guide to life complete with its contradictions and schisms and interpretations. Moreover, 1400 years have passed since the advent of Islam and it has gone through multiple ages.
I’ll even say this — do you think that a person who identifies as a neo-Nazi does not love his kids or his wife, does not care for his pets or do the normal things necessary for a human being? Of course he does.
But there are times when the ideology and the person become nearly synonymous, because the ideology swallows the individual’s personality whole. An example would be Osama Bin Laden, who is synonymous with terrorism, and in all his public persona at least, only spoke about and propagated terrorism. In this case it is not possible to look at Osama bin Laden the person as separate from radical Islamism the ideology. He IS an ideology, in a certain way.
The other example of course, for the purposes of our discussion is Adolf Hitler. One cannot meaningfully visualise Hitler in any context other than his ideology and the horrors it perpetrated.
In this sense Nazis are a bit closer to the ideology than Muslims — because for most people who identify as Nazis, their ideology at least partly encompasses their life goals (goals being the key part here, not ‘life’).
A better analogy for Nazis would be Islamists. Which means, political Islam.

Anyone who reads this is welcome to give their inputs on this issue.