Considering the anti-clerical violence and outright banning of church activities during the first decade of the PRI regime, the Catholic Church has effectively been neutered as an anti-government entity.
Don't ever make the mistake of calling Mexico a "Catholic" country, particularly in terms of its politics. The government for many years was run by atheists/agnostics (Vicente Fox being the first openly Catholic president in decades when he was in power), and the 35% of the population that is culturally Amerindian practice a fusion of paganism and christianity.
Points taken.
However, I was talking, mainly, about the clerics in the USA being rather stupid on these issues.