Up until 2009, the word “right-wing” was not used in the definition of Fascism or Naziism.
Both of these ideologies were socialist movements. Not sure how you can construe that to be right-wing.
Fascism is a totalitarian movement that empowers an omnipotent government to control every nook and cranny of political, economic, social, and private life – generally in the name of “the public good.” Its leadership is commonly spearheaded by a powerful, charismatic, even deified figure who is viewed as uniquely capable – along with his hand-picked advisers – of leading his nation to new-found or restored greatness. Its economics are collectivist, socialist and redistributionist – supremely hostile to free-market capitalism and wealth inequalities. And it tends to promote and exploit the grievances of “the common man,” portraying society as the theater of a ceaseless conflict – a class war – between oppressor and oppressed, victimizer and victim. Consequently, identity politics are central to fascism.
Does that sound like right-wing politics?
How about this quote from Mussolini:
“All within the state, nothing outside the state, nothing agaisnt the state”
― Benito Mussolini
Does that sound like Republicans or Democrats?
Or how about these?
The foundation of Fascism is the conception of the State, its character, its duty, and its aim. Fascism conceives of the State as an absolute, in comparison with which all individuals or groups are relative, only to be conceived of in their relation to the State. The conception of the Liberal State is not that of a directing force, guiding the play and development, both material and spiritual, of a collective body, but merely a force limited to the function of recording results: on the other hand, the Fascist State is itself conscious and has itself a will and a personality — thus it may be called the “ethic” State….
…The Fascist State organizes the nation, but leaves a sufficient margin of liberty to the individual; the latter is deprived of all useless and possibly harmful freedom, but retains what is essential; the deciding power in this question cannot be the individual, but the State alone….