Yes. And, a Republican could join the Democrat student group, and if he got enough of his Republican friends to join with him, he could conceivably lead the Democrat club.
My experience with similar funds years and years ago is that there's a student governing board that makes recommendations to the "faculty advisor" who authorizes disbursement. Since this was a very corruptible situation the campus dormitory systems had managed to exempt themselves from the situation years before ~ with, it turns out, special legislation provided by the state legislature.
There's no reason the State of California could not now EXEMPT students from any obligation to participate in the "the student activities fund" through payments of fees for that purpose ~ provided they don't belong/participate to/with any of the groups receiving funding.
In fact, there's probably already a law on the books somewhere just waiting to be found that in fact exempts non-participants from the obligation to pay the designated fees.