"At the time, people who opposed communism were considered reactionaries." No. Nazis had an open ambition to end the Weimer Republic - a liberal democracy - and a reactionary was anyone who opposed their radical agenda i.e. people who believed in the Weimer Republic.
"nationalists don’t typically describe their opponents as reactionaries" These ones did. The Nazis had a lot of changes in mind and had bones to pick with anyone who wanted moderate changes that could be implemented through democracy.
"Furthermore, the Nazis wanted to suppress religion" This is by FAR the most ignorant thing you've said. The Nazis had 3 clear instructions to German women: Kinder, Kirche, Kuche: have kids, go to church, and cook dinner. If you didn't know that, you CANNOT lecture people on Nazi history because that is Nazi Germany 101. The Nazis saw the Protestant church as a traditionally German institution and they wanted to put it at the center of every German household. Whoever told you that the Nazis suppressed religion was just flat-out lying to you.
"many of the Jews murdered in concentration camps were capitalists." Well done, genius, many of the Jews in Germany were capitalists, but then, Germany was a capitalist country. Many of EVERYBODY were capitalists. Including the big businesses that backed the Nazi party.
Everything you are writing is incorrect nonsense not supported by the clear records of history. National Socialists were and are ultra-nationalist, socially conservative, anti-egalitarian and fascist. They do not belong on the left wing. They are squarely far-right.
Hitler on April 12, 1922, speaking at Munich: "There are only two possibilities in Germany; do not imagine that the people will forever go with the middle party, the party of compromises; one day it will turn to those who have most consistently foretold the coming ruin and have sought to dissociate themselves from it. And that party is either the Left: and then God help us! for it will lead us to complete destruction - to Bolshevism, or else it is a party of the Right which at the last, when the people is in utter despair, when it has lost all its spirit and has no longer any faith in anything, is determined for its part ruthlessly to seize the reins of power - that is the beginning of resistance of which I spoke a few minutes ago. Here, too, there can be no compromise - there are only two possibilities: either victory of the Aryan, or annihilation of the Aryan and the victory of the Jew."