Mexico does have a separation of church and state wrt to their weddings. IIRC you need 2 separate officiators for a religious wedding - one from the church and one from the state. (Nearly got married to a Mexicana some years ago.)
I'm remembering a well known political cartoon from the 20s or 30s, where a pig-like priest in the confessional is telling the poor campesinos, "Obey your padrone and work hard and you will get the 10,000 indulgences."