How has this happened? What are your concrete examples of this having happened?
I suspect all of the example(s) you might have are going to be overblown news storie(s)
But if there are decades of this, I'd love to see the evidence.
Mandatory political indoctrination courses is the biggest thing. But also, having to fund left-wing events with mandatory activities fee. And it was much easier to get funding as a student group if you have the correct political opinions. Finally, if you say the wrong things, you might get reported to a political commissar (this was really rare at my uni though, there were signs everywhere saying how to make a report but in practice people didn’t do it).
I don’t know that Universities cower before leftist ideology. They are leftist, and are the generators of leftist ideology. It’s more like the wallow in it than cower before it.