If a county included in this part has adopted the County Financial Management System of 1981, compiled in chapter 21 of this title, the County Budgeting Law of 1957, compiled in part 1 of this chapter, or private acts, and such county does not revoke or repeal such act, in the event of a conflict between this part and such acts, this part shall not supersede those acts, except that § 5-12-210 shall supersede any other law.