My immediate answer to this is “why would they think that when Imrahil is out there actively campaigning to be the most popular man in Minas Tirith”, honestly? I know it’s sort of a popular theory in the more Gondor-centric parts of the fandom to hold that Gandalf at the very least really looks like he’s planning a coup, but I think that the evidence is significantly more in favor of Denethor’s brother-in-law as the brain behind that particular goal.

More or less off the top of my head:

• Imrahil is of a royal line that’s at least equal to the House of the Stewards, with a stronger claim to leadership depending on how you look at it (specifically, Gondor will never accept a Steward becoming King, but Imrahil is a Prince in his own right and holds a hereditary office that has as much history and pedigree as the currently-absent throne would require)
• Imrahil tells Aragorn during “The Last Debate” that he has several thousand men, including foot soldiers, waiting at home; he did not bring these people when his lord called the banners. You can argue that there are legitimate reasons for it, sure, but it’s also awfully convenient that he has an army waiting in the wings to be summoned north to Minas Tirith
• When Faramir is rescued by the swan knights, watchers presume that Denethor ordered a sortie, but this is never explicitly confirmed in-text. What we see is Imrahil on the front lines saving his nephew and the men who went with him, and whether or not he’s actually the one who gave the command is up in the air.
• Unlike Denethor, he’s actively trying to befriend the ordinary people in the army. He and his men are out on the battlements singing and working to boost the spirits of the soldiers, and are making sure they’re seen doing these things. That looks an awful lot like an attempt to garner goodwill and create camaraderie with the common folk.
• He’s popular, he’s rich, he’s royal, and Denethor is the reason his sister died. People have started coups for less.

What I mean is - yes, absolutely, I’m certain that people think Gandalf did something to get Denethor out of the way, but I think they assume he did it in cooperation with Imrahil (who, in this conspiracy theory, knew Aragorn was coming - he sailed up the Anduin, Dol Amroth had to know!) instead of what “really” happened, which is that Imrahil had a full revolution he was planning and then his brother-in-law set himself on fire and made all the plans moot.