In actuality Stanford in many way is more liberal than Berkeley. As a private college they were able to kick ROTC off campus and deny the CIA, etc. opportunities to interview potential future employees. Berkeley being a public university had to maintain its ROTC program and keep its job interview support open to all government agencies.
Stanford has the gay liberation "statues" on campus, has leftist deans, and something called The Firehouse that houses unironically the most flaming students on campus.
They also have a Blacks-only dorm called Ujamaa that MLK, Jr. would have found confusing.
It's a great place for students from nominally conservative backgrounds such as Indians and Asians to get indoctrinated with Marxist nonsense before being employed by the likes of Google, Amazon, and Facebook.
You’re right. Stanford, as a whole, is as liberal/left as it gets. The Hoover Institution is the lone exception, employing a mix of liberals, moderates and conservatives (e.g., Victor Davis Hanson). As such, much of the university is in a constant state of war against Hoover.