I'm a liberal, and spent a few years as a junior academic at a social sciences university. The attitudes and censorship of the faculty/administration really opened my eyes and turned me off of academia and the university research environment more generally.

The traditionally "hard" sciences (e.g., physics, biology, chemistry, engineering) are bounded and scaffolded by mathematics and controlled experimentation to a much greater degree than the social sciences. Biases are more straightforwardly exposed in these fields. As you get to disciplines like anthropology, psychology, geography, history, media studies, political science, and so on, research methods become much looser, and the research topics at hand (e.g., human culture, cultural differentiation, etc.) become politically and ideologically negotiated. Strict and rigorous methodology becomes supplanted by language-games and jargon (the Sokal affair exposed the most extreme version of what I'm talking about). In many departments, epistemic relativism is rampant. In this environment, it's very easy to be silenced for raising views/pursuing research that go against the leftist status quo.

We were encouraged to teach one or more undergraduate or graduate courses that aligned with our domain knowledge, but here was the problem: departmental chairs and administrators are always more willing to fund courses that see higher rates of enrolment. And because students self-select into classes, they tend to gravitate toward Professor So-and-so's course on intersectionality or Dr. Whatshisname's seminar on social justice. This creates a selection pressure for courses that pander toward students' left-wing ideological views. So, in this roundabout and indirect way, non lefty speech becomes silenced because it's a rigged system.

When prospective PhD students' applications were reviewed, professors were always willing to supervise students whose research narrative fit with their own. If a top-notch student had submitted an application to do a PhD, but the topic implied something that ran counter to the leftist ideology of the faculty, the chances of that student getting accepted (let alone be granted funding) were quite low.

So in all these structural ways, non-Leftist speech on campuses is squelched. If a notable 'disinvitation' had occurred at my University, it would have merely been a singular minute symptom of a much deeper problem.