Actually the Mexican president in the late 1920s Plutarco Calles was pretty much a Fascist, saw Mein Kampf as a the zeitgeist of 20th century thought and had uniformed thugs roaming Mexico City. All this despite being part of the apparently left-centre National Revolutionary Party, which under him had some pretty authoritarian and corporatist ideas.
After he was forced to step down due to Presidential one-term limits in the constitution, he dominated the party as a shadow dictator, until Cardenas appeared in 1936 as President, despite being an old comrade and a PNR loyalist he was also a pretty dedicated Social-Democrat and ochestrated a major internal coup that removed business, union and political leaders that were loyal to Calles' fascistic ideas. Ironically Calles had picked Cardenas as a safe puppet to rule through.
Have someone else picked as PNR candidate in 1936 (which guaranteed him the Presidenacy in post-Revolution Mexico) to rule through and a Vargas style shift might see Mexico become a fully-fledged corporatist state.
Still such a country would side with the Allies regardless due to America's unfluence, just as Brazil did (something Hitler thought impossible due to ideological ties)