I spent roughly 37 years in public institutions of higher education in California - as either a student or faculty member - and the allegation of leftist bias is absolutely correct. I spent another 5 years in the public institutions of higher education in other parts of the country and the leftist bias was there too, no surprise.
However, I don't think the beliefs of most students are much influenced by leftist professors. A few, yes; most, no. Unfortunately it is the few who are influenced who go on to become the next generation of professors. Perhaps we shouldn't be surprised about this, either.
Remember the quote correctly attributed to French Premier Georges Clemenceau (1841-1929), but often attributed to Sir Winston Churchill:
Not to be a socialist at twenty is proof of want of heart; to be one at thirty is proof of want of head.