That's certainly one way around it
Instead of just saying "butterflies," you might want to post something more substantive. I hear a lot of talk of "butterflies" and nobody actually presenting any scenarios other than, "Catholics would go to a Catholic country because Catholicism."
Seriously, why would the Irish go to Mexico in larger numbers than America? Shared faith does not mean cultural or linguistic connections, and those two trump sectarian similarity. Also recall that while anti-Catholicism was the norm in the US, the State rarely (if ever) shut down Churches because "ew, Papists," and the worst things got were urban riots.
Mexico also has a troubled history between its Church and secularists trying to curb the medieval excesses of the clergy. How to butterfly that inevitable confrontation? Or the fact that Mexico's quality of life is far less than that of the United States. Unskilled white workers are also going to prove troublesome to Mexico's racial caste system.
Many of the German Catholic immigrants were farmers; where are they to go but the already-populated zones of Mexico? And don't say Texas, because the Germans who settled there OTL preferred the Americans.