Weren't romans the original fascists by the definition of the word, and Legion is LARPing as them. I don't understand their thought process.
Long-winded response here. It's also a layman's response, I'm by no means a proffesional, and if anyone is they can feel free to correct me on any details I might get wrong:
It's kinda inherently anachronistic to try and call Classical Era states "Fascist" after 20th century ideologies which did not yet exist.
Perhaps you could see parallels, but given that Rome existed from 753 BC to 476 AD and had a constantly changing political landscape for the period it was around, you could probably find evidence of Rome being whatever political ideology suited your personal interpretation of it, given the timescale and all the major political upheavals that happened within it.
Mussolini tried to play up a lot of the Roman Heritage of Fascist Italy, especially through public artworks, but this was largely an aesthetic technique used to try and justify fascism by using past states.
There's multiple arguements you could make against Rome being fascist:
Firstly being that to talk about Rome having a singular political ideology at all is inherently misleading: Rome started off as a Kingdom, which was overthrown to make a Republic, which was overthrown in to a Dictatorship again, which then after a period of Civil War became a weird semi-democratic semi-dictatorial structure under Augustus, followed by centuries of Emperors, convrted to Christianity and then eventually deciding to partition in multiple different ways, eventually settling on the East/West divide. Some Emperors were also Philosophers, writing their own treatises on what government meant, most famously Marcus Aurelius who wrote extensively about Stoic philosophy. To make a case like "Rome was Fascist" or "Rome was Liberal" or whatever, you'd have to make the case that every single period of Roman History, or even the governing styles and philosophies of every single Roman Emperor conformed to that idelogy.
Secondly, what we usually associate with Fascism is it being Xenophobic, Ultranationalist, Hyper-Authoritarian and Hyper-Traditionalist. Now, you could make the case for Authoritarianism, though I'd respond that making that case would be a flawed analysis given that Rome existed prior to modern conceptions of liberalism and human rights, so arguably all of Rome's neighbours would also fall under that definition, and given that since the Republic period Rome had Civil Law, Courts, the right to Trials, ect., it was arguably less authoritarian than many of it's contemporary states.
As for the Traditionalism and Xenophobia, the Romans had much more of a "Whatever works" approach to traditions and other cultures, their attitude shifting based on what suited their needs. There are cases for instance, of them engaging in Genocide. Typically though, the Romans were much more likely to respond to conquered cultures by adopting their traditions and intergrating them in to the structure of the Roman State: because y'know, this is actually a very efficient way to govern a vast empire that incorporates multiple different cultures: typically cultural inclusion makes your imperial subjects less likely to revolt. If modern Fascists held the same beliefs they do today, and lived in the Roman Empire, they'd probably be disgusted by how regularly Rome changed it's traditions to incorporate conquered cultures.
You could make the case that individual figures had ideologies which resembled a form of proto-Fascism. The figure I'd make the case for is Augustus: He never took on any official monarchial titles, rather insisting on being called "First Citizen" or "First among Equals", while at the same time using his sway in the Senate to be granted several lifetime positions as a Commander, Tribune and Censor, and regularly considered himself more as a speaker for the Roman people rather than a leader. This is kinda similar to the structure of Fascism: dictators placing themselves in power indefinitely, but the propaganda not treating them as such but rather as voices of the Nation(which is of course, inherently circular: you claim to speak for the nation, yet are yourself deciding what the nation constitutes and believes).
There's also the fact that Literature during the Augustan period tended to have pseudo-fascistic qualities when discussing natures of the state: the Poet Virgil famously wrote philosophical treatises about human beings and natural subservience to authority using Bees as an allegory, which resembles Fascist political ideology quite strongly. He also wrote the Aeneid: an attempt to replicate Greek Epic Poetry, which situated Rome as being descended from the survivors of Ancient Troy, in an attempt to justify Rome as being a consistent state that followed from the traditions of Heroic Era Greece(Which was at the time was considered the height of civilisation). This is another trait of fascism: trying to tie yourself to some ancient great civilisation, and treat your rise to power as an attempt to recreate that civilisation.
However even with all this in mind, it would still be something of a misnomer to call Augutus a fascist, given that the Augustan period had very different goals to modern Fascism. Modern Fascism tends to be reactionary and traditionalist, whereas the Augustan period was more about re-establishing what Roman Governance meant in the wake of the collapse of Republicanism, and decades of Civil War.
Anyway, one thing that I think's an interesting take-away from this is that what makes Legion a good faction in New Vegas, IMO, is precisely their selective reading of Roman History. It kinda rings true to actual Fascism. Mussolini did the same thing, taking aesthetics he liked from Roman History and using them to imply a rebirth of ancient civilisation. That's kinda the whole point: Legion, like all fascists, kinda ignore the vast scope of the historical era they're dealing with, and instead summarise it as sort of "Whatever personally suits our claims to be the successor to this civilisation"
Also: You're right in pointing out the irony of the modders not letting you play as the Enclave because they're fascist, but also not considering the Legion as such: given that JESawyer has actively stated that he wrote Legion around Umberto Eco's essay "Ur-Fascism", an essay about the inherent contradictions in fascism.
Like, when literally the designers of the game said they wrote Legion around being showcases of the contradictory nature of fascism, it's hilarious that the Frontier modders are acting as though that's not the case.