As an amateur student of Mexican history, I am not for sure what he would be talking about. It has never been the case (until perhaps very recently), that the government of Mexico has adopted a policy of seperation of Church and state. Actually, quite the opposite, successive governments of Mexico, with perhaps the Diaz dictatorship being a little more lenient, since the break away from Spain have always tried to keep the church under its complete control. It confiscated Church property, schools, hospitals, land and pretty much gave most of it away to cronies. It tried to force priests to be employees of the state. It limited the number of priests per districts based on population levels. It banned foriegn born priests. It banned clerical dress in public. All of this happened time and time again. It has always been very anti-clerical and very anti-religion. The government of Mexico in the 19th century and early 20th century chose an uneducated population over a population educated by the church. Not any type of seperation of church and state we would recognize. BTW, time and time again, the US government sided with the oppressors. There was finally a Catholic uprising in the 1920s, the Cristeros movement, many of the leaders for this movement were martryed. I suppose there has been instances of people excommunicated by the church for supportting the anti-catholic policies of the state, that would not surprise me. But this is hardly being excommunicated for supporting seperation of church and state.
If the professor was talking about the history of democracy in Mexico, it must have been a very short talk, as there is not much history to speak of.
Through it all, the Mexican people kept their faith. Of course, they had the Blessed Virgin looking out for them.
In general, think of the Mexican government’s attitude towards religion much more closer to what you would know about the Soviet Union as opposed to what we have experienced in the US. May I recommend this book, although written in the 30s, it is quite good:
amazon.com/Blood-Drenched-Altars-Francis-Clement-Kelley/dp/0895553198