Texas A&M is the very conservative public university of Texas. It started as a male military academy with the purpose of graduates entering the US military. The Aggies favorite son is Earl Rudder who commanded troops during the invasion of Normandy.
UT Austin is the liberal public university in TX. It was famous for its hippies back in the 60s.
So, my mental model of American conservatism (I'm not American) was always that they were _relatively_ thick-skinned as right-wingers go; George W took a fair bit of public criticism, say, without seeming to get particularly upset about it. Trump didn't react well to criticism, obviously, but he's kind of a baby, and a bit of a special case; extremely privileged and not a career politician. I've got to say I'm kind of surprised that the rank and file are so sensitive; I kind of thought this was largely _gone_ in western democracy. Feels very, very old-fashioned (or, as mentioned, Soviet).
I sometimes wonder if I'm missing something fundamental about how Americans think. This behaviour would be interpreted (beyond being anti-democratic, but parts of the right wing won't necessarily care about that) as showing extreme weakness here. Like, to the extent that a politician wouldn't do it, even if they _could_, because would be very politically damaging; "my opponent is a weird baby" is a stupid talking point to hand to your opponent.
I can't speak on modern American conservatism as I am not one. Looking from the outside, I would chalk this one up as part of the culture wars that is fueling the conservative movement, rage against "critical race theory" etc.
FWIW, George HW Bush is buried next to the Texas A&M main campus. There is also a school of foreign policy named after him there. Both Bushes, the father and son, cultivated an image of a likable goof, even if you differed with their politics, were someone you could go to a baseball game with and shoot the breeze over a couple of beers. The modern conservative movement is not like that.
UT Austin is the liberal public university in TX. It was famous for its hippies back in the 60s.