On Jan. 19, Angelica Berrie sent an email to Nemat Shafik, the president of Columbia University. Ms. Berrie reported that the Russell Berrie Foundation, named for her late husband, had scheduled three grant payments to Columbia.

But after months of campus protests around the Israel-Hamas war, Ms. Berrie also delivered a warning.

As the foundation prepared to transfer almost $613,000, Ms. Berrie told Dr. Shafik that future giving would partly hinge on “evidence that you and leaders across the…