I don’t know of any law that would prohibit it.  A (c)(3) is not a governmental agency that would be prohibited from imposing a poll tax.

The key question is whether the voting members are willing to accept the imposition in order to vote.  If enough of them don’t like it, they can try to change the directors, or the bylaws, or whatever other method of determination requires the election to be held at a banquet where voters have to pay.  There may be a way to allow “absentee ballots” or other means of voting without paying for the meal.  They may be willing to hold the elections at another time, or in another way.  But ultimately I think it depends on what the members want to do.  It is all about counting the votes.