The incumbent or nominee of each of the following offices shall be an ex officio member of the committee in the county in which he or she resides:
Ex officio members shall be entitled to all the rights and privileges, including the right to vote, and shall have the same standing in every way as other members of this committee, except they shall not be entitled to a ballot designation of incumbent upon seeking election to this committee in the next presidential primary.
Ca. Elec. Code § 7652