The bill, S.5285, was filed in May 2019 by state senator Robert G. Ortt, but was resubmitted in January 2020 to the Senate committee on higher education:
[a.] The state university trustees[, city university trustees, and community college trustees] shall adopt rules that any student group or student organization that receives funding from the state university of New York that directly or indirectly promotes, encourages, or permits discrimination, intolerance, hate speech or boycotts against a person or group based on race, class, gender, nationality, ethnic origin or religion, shall be ineligible for funding, including funding from student activity fee proceeds.
[b.] … “Boycott” shall mean to engage in any activity, or to promote or encourage others to engage in any activity, that will result in any person [including corporations and other nongovernmental entities] abstaining from commercial, social or political relations, with any allied nation, or companies based in an allied nation [defined to include NATO members, SEATO members, Rio Treaty members minus Venezuela, Ireland, Israel, Japan, and South Korea] or in territories controlled by an allied nation, with the intent to penalize, inflict, or cause harm to, or otherwise promote or cast disrepute upon, such allied nation, its people or its commercial products.
But when student groups or organizations get generally available funding from public universities, the university must distribute this money in a viewpoint-neutral way, see Rosenberger v. Rector (1995) and Christian Legal Society v. Martinez (2010). That means that the government can’t exclude speech that “encourages … discrimination, intolerance, hate speech or boycotts.” (Discrimination against allegedly bigoted speech is of course viewpoint discrimination, see Matal v. Tam (2017).)
A rule that government funds can’t be used by a group to actually discriminate, or to actually refuse to deal with particular firms, would be constitutional (see this post), because it would be a restriction on conduct (discriminatory refusals to deal) and not speech. But restricting promoting or encouraging discrimination and boycotts is restricting speech based on viewpoint.