Yep, what Simon said. Disconnect the white and keep the tip insulated.

Mixing different brands of pickup can often result in out of phase combos. You can’t reverse the neck pickup due to the way it’s made, so the Bridge’s red (+) and black (-) are your reverse option. The Bridge pup’s bare braid should stay connected to ground and once the white is disconnected and insulated test the middle position of the switch. If it still sounds out of phase then just swap the red and black connections.