Mexico is indeed militantly secular. More so than France where Jewish schools get government funding. The government of Mexico regulates the curriculum even in religious schools.
The white in Mexico’s flag did indeed initially represent the Catholic faith. The Spanish had been burning Protestants and Jews at the stake until shortly before independence in 1821. But religion and state were separated in 1857 and that remains the case today. A Jewish woman is way ahead in the polls for the Presidential election later this year.
Church and State have been separate in the US since 1833.