There is no ignorance of history or any of the other nonsense that you mentioned, in knowing that almost the entire Mexican population about 98% were fully baptized, members of the Catholic denomination.
Regardless of what they were fighting for, it was Catholics fighting, if intervention was called for, there were many almost purely Catholic nations south of Mexico to intervene.
What do you call it, then? Plutarco Calles was raised by an uncle who was a fanatical atheist who hated Catholics and Catholicism. When Calles became President of Mexico, he effectively made Catholicism illegal, and received awards from Freemasons for doing so.. Priests had to go underground; some were arrested and executed. Since you didn't know about any of that, I'd say maybe you should consider the possibility that there is a little ignorance of history in play.