Brooklyn College professor Mitchell Langbert sheds light on that question in this post. The “Professional Staff Congress” that purports to represent Langbert and other faculty members while taking their dues money through compulsion (New York is not a right to work state, so no one can say, “sorry, not interested” to the union) and using it for a host of blatantly political uses. Among other things, it gives money to political organizations like the Working Families Party.
Union apologists claim that if dissidents like Professor Langbert were not forced to pay union dues, that would permit them to be “free riders.” But in his view, what the union does is far more harmful than beneficial (perhaps even infinitely so) to him, he is a forced rider. Thomas Jefferson once observed, apropos of government sponsored religions, that it is “sinful and tyrannical to compel a man to furnish money in support of ideas he does not believe.” That point applies with equal force to compulsory unionism.