All students are entitled to equal access to education — free from harassment and discrimination on campus. Public and private universities are bound by civil rights laws to protect students from discriminatory harassment on the basis of protected characteristics, including race and national origin. So, while offensive and even racist speech is constitutionally protected, racist speech directed at a particular student can constitute impermissible harassment, not free speech.
The Family Educational Rights and Privacy Act (FERPA) prohibits universities that receive funding from U.S. Department of Education programs – which generally covers both public and private universities – from disclosing many types of student information without your consent if you are 18 and over. The law does allow a school to share “directory information” like a student’s name, address, telephone number, degrees, awards, and participation in activities and sports.