Like lots of inconvenient history, the Mexican Cristero War doesn't get much play from Hollywood. It never has. In 1924 the new Calles government, which was a cabal of assorted anti-religious fanatics (Calles and many of his subordinates were Freemasons) saw their big chance to end the Catholic Church in Mexico once and for all. Thus commenced a state policy of systematic and sometimes violent oppression of Catholics - who finally rose up in armed opposition to the government.
Concerned about their Mexican oil holdings, Freemasons in the US government saw to it that the US supplied the Calles government with men and materiel, even providing some fighter planes, during the war.
In 1929, after three years of fighting, an agreement of sorts was finally brokered by the US and pressure was brought on the Pope of the time, Pius XI, to get the Cristeros to lay down their arms - which many of them did. The Calles government then repudiated its part of the truce and killed thousands of Cristeros in reprisal executions.
In the end, though very circumscribed, the Church in Mexico did survive the onslaught and has in a certain spiritual sense prospered. Mexican seminaries are full and Mexican Catholics are much more devout than their Euro/American co-religionists. One edifying story confirming this tells of some starlet, whose name I forget, filming a movie down Mexico way. She and her boyfriend of the moment got amorous atop the portico of a church. The locals took offense at this and began hurling rocks at them, yelling "Go home, slut!" That kind of indignation would never have happened in the US or Europe.
Anyway, For Greater Glory IS a Hollywood production, so expect, in spite of what the trailer indicates, for it to become another angry swipe at Catholicism. Anyone wanna take that bet?