It's important to understand fascism in its historical context. Mussolini and Hitler used a complex of political, social, cultural, and economic ideas to seize and maintain state power. David Neiwert has done a lot of historical work on precisely what they did and how they did it.
But in another sense, I think it's important to analyze not just what fascism is or was, but what precisely we don't like about fascism. To no small extent, the specific ideas that the fascists promoted are historically contingent. They did what they did because material conditions in Italy and Germany in the 1930s made those specific ideas especially useful and effective. But it is no longer the 1930s, and the United States is not Italy or Germany, so we could relax some of the specifics of what fascism was, and concentrate on what was more generally bad about fascism.
So, for example, one element of fascism is subordinating the ordinary individual to the state, and the state to the Great Leader. If we're going to define fascism as the more-or-less "essential" elements of what Mussolini and Hitler did, this kind of subordination is pretty essential, and if someone we don't like doesn't have it, whatever they are, they're not fascists.
And on the other side, I personally don't want to subordinate myself to the state, but if that's what people want, why shouldn't they have it? Human individuality is at some basic level ineluctable, so if people were to individually choose to think of themselves as elements of the state, they are still actually individuals.
But what if the masses of Germans and Italians didn't actually choose to be good fascist citizens? Then our criticism wouldn't be that people chose some way to live that we personally don't like, but because the fascists violated the more general principle that people should exercise substantial freedom of choice. I'm not an historian, and I haven't studied the history of 1930s/1940s Italy and Germany in any detail, but from my cursory readings, it does seem that Italians and Germans didn't really choose to be fascists, but were intimidated into tolerating it.
And thus we can drill down into what's really bad about fascism in a more general way: legitimization of state power directly by violence. A regime is "fascist" in this sense to the degree that it maintains its legitimacy directly by its ability to perpetrate violence against its subjects, and not by its promise (even insincere) to maximize the well-being of its citizens. "We are the legitimate state," says the fascist, "because if you don't call us legitimate, we will beat you up or kill you." Such a state is a real state, it has legitimacy, but perhaps that's not the sort of legitimacy that we want.
Note that "legitimacy" in this sense is not the idea that some regime is legitimate by virtue of being the first unconstrained choice of almost all of its subjects; a state is legitimate to the extent that its subjects do not organize to oppose the state's monopoly on violence.
This idea subtly differs from the idea that the a state may legitimately use violence. Fascism is not the use or threat of state violence, but the establishment of legitimacy by means of violence. It is possible for a state to use considerable violence on its subjects — e.g. to punish unacceptably deviant behavior — so long as the mass of citizens legitimize that use on a non-violent basis. For example, people still murder their neighbors, and the state violently captures and punishes these people, but the prohibition on murder, and the state's legitimate use of violence to enforce that prohibition, is established morally and socially, not violently.
In this sense, then, a regime can be fascist to a greater or lesser degree, and can be more or less fascist towards different subsets of its population. So, for example, the American South* was absolutely fascist towards the black slaves, obtaining its legitimacy exclusively by its ability to perpetrate horrific violence against the slaves without organized opposition, and quite fascist against many white people, willing to use quite a lot of violence against white people who even hinted at opposition to slavery. In the South, slavery and the slave state was legitimate because any organized opposition to slavery was suppressed by violence.
*With the usual disclaimer that I'm not an historian of the antebellum South.
To a certain extent, it doesn't even matter that, in a climate of legitimacy-by-violence, some subjects will internalize what is supported by violence. Presumably, if the vast majority of citizens support some idea, it is unnecessary to use violence against a few idiosyncratic opponents. We do not, for example, presently hunt down and kill people who advocate biblical theocracy, despite this idea being completely contrary to our notions of a democratic republic. Thus we can infer that either opposition to slavery in the South was actually a majority*, or that allowing a minority to express opposition to slavery threatened the legitimacy of the Southern regime. Hence the South was strongly fascist.
*Of white people; we can confidently assume that almost every black person was opposed.
And too, the present neoliberal regime is quite fascist towards black people. At every level from local to federal, black people know that to effectively oppose state oppression of black people in any way means death. Organized opposition to racism is thus suppressed directly by violence. Organizations such as Black Lives Matter are tolerated only to the extent that they are ineffective. If BLM were to actually threaten the racist state, their leaders would be jailed or assassinated and their membership dispersed or slaughtered. (Most likely, BLM will be co-opted, their leaders inducted as junior members of the servants of the neoliberal ruling class, and the fascist violence against ordinary working-class black people will continue unabated.)
So too could socialists become fascists in this sense. A socialist state would be fascist to the degree that its legitimacy were established and maintained directly by violence. One of the core principles, therefore, of socialism should be that its legitimacy should never be established by violence, that socialism is absolutely anti-fascist. We must persuade the great mass of people that socialism is better, not that we have the soldiers and bullets to make people socialist, like it or not.