While Rutgers is a state university, you can bet your bottom dollar that it takes federal funds, like virtually every other university in the US. I think only 1 or 2 colleges refuse federal funding, IIRC, Hillsboro and/or Grove City. Also, Rutgers students accept federal financial aid, so it would be subject to federal law suits as well.
No doubt about that.
But its officials can be sued in federal court because it is a state institution on the theory that they are in violation of the "equal protection" clause of the 14th Amendment of the US Constitution.
Recall that the "equal protection" clause applies to states and their agencies (including cities and counties, BTW, since they are creations of state government) only, but not to the federal government. Historically, the "equal protection" clause was the basis for, e.g., the Brown case vs. Topeka, Kansas regarding school segregation and the more recent cases against the University of Michigan (a state university) with respect to affirmative action in admission policies.
The point is that the fact that the university takes federal funds isn't a prerequisite for suing them in federal court. The suit can be filed in federal court on federal constitutional grounds alone.