Fascism was not "reactionary". It was, in many ways, a sibling ideology to 'communism', but with glorification of violence, a broadly "irrational" (i.e. explicitly anti-intellectual, and almost relishing in the use of blatant propaganda as a means of influence) attitude to mass politics and either nationalist or (in the more extreme Nazi version) racially-supremacist ideology as major selling points. "White nationalist" is somewhat inaccurate as you point out but "reactionary" is totally wrong, and Soviet propaganda is the only reason why some people today still think of fascism as "conservative" or "reactionary".
It is absolutely reactionary, but it's a reaction against enlightenment thinking. This explains many of its key attributes: Use of propaganda, anti-intellectualism, and rejecting egalitarianism.
It's also why it's not easily dispatched by enlightenment thinking... it survived those battles back in the 20th century and ultimately had to be put down with exercises of power (often military, sometimes social, rarely diplomatic).
Fascists gained power in Italy, Germany, and Spain as a direct result of anti-communist sentiment (and in the case of Germany, a failed communist revolution). Mussolini's early writings were directly proposing nationalism as the answer to communism's failures. Everywhere fascism had success it was because it was pitted against the threat of communism. I don't know how the rise of Fascism was anything but reactionary.
I agree that facism's rise was tied to nationalism's rise.
But we're talking about the root causes of WWII. And one of the Nazi party's specific goals when invading Poland was to exterminate the Jews and Roma (Gypsy) populations of Europe.
