How was Arnie Vinnick a Republican

My understanding was that people identify themselves as republicans (or a democrat) based on the values that they align the best with. Vinnick is pro choice, gun control advocate, centrist on immigration. Only supported tax cuts and arctic drilling, supposed Republican rhetorics . Not enough to espouse republican nominee, imo. I am watching the West Wing for the 3rd time. Seemed fitting now in wake of election season.