The council shall elect from its membership a chairperson and a vice chairperson each of whom shall serve for a term of one year and who may be reelected. Membership on the council shall not constitute holding a public office and members of the council shall not be required to take and file oaths of office before serving on the council. No member of the council shall be disqualified from holding any public office or employment by reason of appointment or membership on the council, nor shall any member forfeit any such office or employment by reason of appointment to the council, notwithstanding the provisions of any general, special or local law, ordinance or city charter.