The PRN for some reason or another does not grow more left wing between 1928 and 1934 (idk how to make this happen other than perhaps have a stable presidency with Alvaro Obregon, but that would hurt my POD). As a result, rather than nominating Lazaro Cardenas del Rio for president in 1934, the PRN nominates Plutarco Elias Calles (who was president from 1924-1928 and has ruled the country as "Jefe Maximo" since 1928 with the presidents as his puppets). Calles wins the election, and the right wing of the PRN, combined with the Gold Shirts, turn Mexico into a fascist state. Calles is soon made "Jefe Maximo" officially by Congress, which he then deposes, and leads Mexico down a similar path to Hitler. As there weren't very many Jews in Mexico though, I think communists would be the main enemy here, but I can definitely see a Calles-run Mexico allying with the Axis.
Fun fact: Calles was reading Mein Kampf when the troops Cardenas sent to arrest and deport him captured him.