The most successful student groups leverage their alumni’s monetary influence. Protests and bad publicity for a university are one thing, but money talks and creates real policy changes.
Every university, even public ones now, are heavily dependent on the generosity of voluntary donations, especially from alumni. State universities are now merely "publicly-assisted." Without this private source of funding, many universities simply could not operate as they do now. While it varies from college to college, many alumni have fond affection for their alma mater and take some interest in the overall character and future of it, which is why they donate.
However, most alumni only know what university officials tell them. Most conservative alumni, many of them successful and wealthy donors, would be very surprised to hear how their university has been taken over by the left.