Brazilian Integralism (a type of fascism) was generally not racialist as well.

That isn't true at all. Plinio Salgado was a hardcore Anti-Semite. Just because Integralistas used Black People as tokens in their organization and screamed a Tupi Word instead of "Heil Hitler", that doesn't take the racialist component away from them. They were just Nazis with a Sigma instead of a Swaztika and Greenshirts instead of Brownshirts.

I agree that is silly saying Margareth Thatcher is a Fascist. However, I think you are trying to see too much rationality in Fascists. They do have a certain level of organization, yes, but it's so primal and sometimes so animalesque, most of the things they had on paper went out of the window when they sent the SS/Blackshirt thugs go "crack some eggheads" on the streets. I don't remember who said this, but it's useless trying to understand Fascists too much, because they are Pure Evil and our minds simply have no capacity of comprehending Pure Evil.

Like I pointed out in relation to Brazilian Integralistas, this lack of Rationality from Fascists comes from the fact that they long on contradiction. Fascism itself is a Contradiction. Fascists did everything in their reach to present themselves as an alternative to Socialism and Bolshevism. Always remember that Mussolini himself was a Socialist once. He knew how to appropriate Socialist Rhetoric, especially Class Talk. So the result is a Far-right Ideology with a Left clothing. That's why so many people confuse themselves into thinking Nazis were Socialists.

So I don't see why Modern Day Fascists can't be the complete opposite on some areas in relation to their 1930s counterparts. You're right when you point out in the 1930s Fascists were National Collectivists, but when they declared their hate for Bolsheviks, they also declared themselves Anti-Collectivists. Hitler in Public said bad things about the "German Liberal Bourgeoisie", but when he took power, he needed those Bourgies to create many of the Public Companies that arose during Nazi Germany. The same goes for Mussolini.

That brings another point I think you ignored. Almost a Century has passed since Fascism was created. Fascists will be different this time around. They will not LARP around as Wehrmacht Officers, they will look and sound like normal people in the same fashion Hitler and Mussolini weren't aliens to their time. It won't be like an Alan Moore Graphic Novel.

There are many common axis that unites both Past Fascism and Present Fascism, but they are what they are, axis and not copied-and-pasted information.

One of these Axis that remain active in Fascist thinking is an Anti-Socialist, Anti-Marxist sentiment. See the way the Alt-Right talks about "Cultural Marxism". I think the biggest explanation why Modern Day Fascists are Pro-Market, unlike 1930s Fascists, is because they view the "Free Market" as the biggest weapon against Socialism and the biggest incentive to Class Collaboration. So, different approach, but with the same intentions.

Anyway, if I would give definitions of Fascism, I would use simple definitions like the ones Robert Paxton gives in The Anatomy of Fascism. They are basic and atemporal enough to be applied in any Era.