In the US, Students have First Amendment rights to express themselves. The critical point here is that by walking out they did not prevent any speakers from exercising their own First Amendment rights.
It does not mean we have to respect them for that or be polite about it. That's our First Amendment right.
Cornell is a private university, but it does receive significant government money and some of it's underling colleges are state funded. If it was acting in a way as to obviously disrespect the first amendment, that funding could be revoked.
> Although it's an Ivy League university, chartered as a private institution, it includes undergraduate colleges and schools that receive some funding from New York State. They are sometimes called state contract colleges. The state subsidy results in lower tuition for students who have New York State residency and are enrolled in these colleges or schools
https://cornelladmissions.happyfox.com/kb/article/217-is-cor...