The RC Church is one of the biggest advocates of open borders — for the United States. I don’t see them advocating open borders for Catholic countries like Mexico. They seem to view open borders for the US as the only way the Catholic Church can grow (or keep from shrinking) in this country - by importing Third World peasants. The Catholic Church grows that way - but, somewhat ironically, the Democratic Party even more.
With buffoonish leaders like Dolan, it’s no surprise they can’t increase their numbers from within the US population, so they need more unskilled, uneducated immigrants from Mexico and points south.
You got it. It’s just another side door.