The University's primary purpose for most people is to educate their children. There are major problems with the way it does this currently. It costs a fortune, fails to provide the necessary skills for the modern workforce and, in many ways, has abandoned it's traditional liberal arts focus for one of identity politics, indoctrination, and an anything-goes culture of alcohol abuse and total sexual freedom.
That's conservative, but not particularly partisan. Our schools are in trouble and we're shooting the messenger.
You might be surprised to learn that most conservatives, just like liberals, send their kids to Universities and pay a lot of money each year to do it.
Anyway, as for a research focus, I think there's disagreement on the conservative side over that issue. I think what most concerns them is waste (not actually getting research despite spending so much money on it) and ideological capture. When University leadership all shares the same political beliefs they will sometimes use the research money they're given to fund very political projects.
I think it's entirely rational to want to stop funding a project which seeks to undermine everything you believe in.
A solution would be to refocus on real research and seek ideological diversity.