John Tanner Fairness and Independence in Redistricting Act This bill prohibits a state that has been redistricted after an apportionment from being redistricted again until after the next apportionment of Representatives, unless the state is ordered by a court to conduct such a subsequent redistricting in order to: (1) comply with the U.S. Constitution, or (2) enforce the Voting Rights Act of 1965. Such redistricting shall be conducted through a plan developed by the independent redistricting commission established in the state, or if such plan is not enacted into law, the redistricting plan selected by the state's highest court or developed by a U.S. district court. The bill prescribes requirements for: (1) establishment of a state independent redistricting commission (including provisions for holding each of its meetings in public and maintaining a public Internet site); (2) development of a redistricting plan (including soliciting and considering public comments) and its submission to the state legislature (with public notice of plans at least seven days prior to such submission); (3) selection of a plan, under specified conditions, by the state's highest court or the U.S. district court for the district in which the capital of the state is located; (4) special rules for redistricting conducted under a federal court order; and (5) Election Assistance Commission payments to states for carrying out redistricting.