You'd be hard pressed to find a conservative college dean, non-profit CEO, or even a librarian. There's a belief (which I think is mostly true), that most government agencies are left-leaning in practice if not in appointed leadership. Add to that the growing (perceived!) left-leaning policies in the military and major industrial players, and you might see what they mean.
I'd be hard pressed to find a lefty college board of directors, or CEO.
I'd believe govt agency staffers, since conservatives by and large want to destroy those agencies and not work there.
The military is a weird place and contains multitudes
Well, I guess I'd roll it back to say there have been high profile, widly circulated perceived-to-be-far-left policies pushed or adopted by traditionally not-that-liberal organizations. Like "DEI" in military. It's all over conservative zeitgeist and looks like a massive power creep to them.