The qualifications for membership in a certified party and for voting at a party primary election include the following: The applicant for membership, or voter, must be at least eighteen years of age or become so before the succeeding general election, and must be a registered elector and a citizen of the United States and of this State. No person may belong to any party club or vote in any primary unless he is a registered elector. The state convention of any political party, organization, or association in this State may add by party rules to the qualifications for membership in the party, organization, or association and for voting at the primary elections if such qualifications do not conflict with the provisions of this section or with the Constitution and laws of this State or of the United States.