The not-black-until-this-as-yet-unreleased-film Fremen would probably never have let him do it. They were already waging a guerilla war against the Harkonens. Paul did not become their messiah purely on his own, the Fremen were primed to see all sorts of omens and portents in him, courtesy of the Bene Gesserit tampering with cultures for that purpose. It was on both sides, with the Fremen repeatedly challenging him, and people like his girlfriend taking up the gage on his behalf, so even if he tried to duck the fights, someone else would take them out and inflate his legend.
And the Fremen do it when he orders. They do this stuff because some superstitions and a boy tell them to. Like I said, both sides.

And they listened to him, when their own superstitions should have warned them otherwise. They were the willing instruments of his tyranny. I don't care about that stuff. I really don't care if black people are the villains or the heroes. I do care when the narrative gets a hero wrong, and if I don't have enough of a track record of harping on that in this community, no one does. And I see all the race-obsessed harping on this crap all the time. It was one of the things a lot of them were whining about in Game of Thrones. They were shitting bricks and bursting blood vessels over Daenerys's crowd-surfing on a bunch of darker-skinned people at the end of season 3. Never mind that Westerosi Valyrians were not white people as the real world knows them, and that the Ghiscari of Slavers Bay were people of color themselves, or that Westerosi are not imperialists or colonizers, being of distinctly inferior technology and economic development than most of Essos, just the fact that Darker-skinned People were venerating a Pale-skinned Person gave the PC crowd apoplexy. During season 8, they managed to bitch that so many PoC were killed in the battle at Winterfell, that a major PoC was killed to motivate a white character and that Daenerys' army committing the atrocities that made her Hitler-Barbie were all people of color. These were not MY complaints, except to maybe point out the hypocrisy of the woke posturing of the showrunners. I don't care that Jamis and Harah are black nor would I if Chani & Stilgar also were, though I admit I'm not as keen on Keynes being gender-flipped, but only because I have come to suspect preachy motives behind that sort of thing. If she says all the same lines and does all the same stuff as the book version did, I don't have a problem with her being a her.

But I am not the one who has a problem with the white family coming to a planet of minorities as benevolent saviors, whose compassion and guts and courage impress the natives, and whose surviving family members become religious figures to said diminutive dusky dudes, leading them to victory against their fellow whites power structure. All I am doing is pointing out that Dune is setting itself up for the exact same criticisms that were leveled at Game of Thrones. It might be that they adapt this more in keeping with the spirit of the books, rather than the literal hero-messiah narrative, making Paul more overtly the monster shallow fans refuse to believe he is, but it does not change the fact, that Daenerys at the beginning of "The Iron Throne" was basically Paul at the end of "Dune", except Jon Snow killed her, as Feyd failed, and Fenring and Hawat both declined, to do to Paul. And they are making this movie so that Paul gets to that place just as Dany did - at the head of an army of foreign "other" non-white fanatics (as even Chani & Stilgar still are in this version) who will slaughter indiscriminately in order to overthrow the extant power structure so their jihadist Leader can 'fix' things.