Mississippi Representative Bob Evans (D-Monticello) has introduced HB 760. It says that if an elected official changes parties, or changes to or from independent status, that official is deemed to have resigned.
Probably that bill, if it became law, could not constitutionally be applied to members of Congress. States that have provision for recall of members of Congress have not been allowed to enforce such laws. The same principle would probably apply to party-switchers. The U.S. Constitution doesn’t permit states to end the tenure of a member of Congress in the middle of the term.