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".