I am Sec/Treas. of a non-profit, tax exempt homeowner''s association. There are some people that say that we cannot charge a late fee.

The answer probably depends upon the specific laws of your state and the manner in which the association is set up.  It may be that the association is simply an unincorporated association and the laws of your state do not provided that such an association (not a legal entity in the eyes of the State) does not have the right to enforce contracts, etc.  You may have to incorporate (become a legal entity in the eyes of the State) in order to enforce your agreements.  If the association is a legal entity, it should be able to enforce its agreements.  The purchase of a home within the subdivision should be made subject to the provisions of the subdivision restrictive covenants - including the association's rules and regulation.  Those rules can provide for late charges on dues.  You should confer with a good real estate attorney in your area.  A modest conference fee should clear up any deficiencies in your association's documents.