I'll suggest a compromise: let the Latin church (and any other Christian churches that want to) shelter illegal immigrants under the terms of the ancient right of sanctuary. Those sheltered have to remain in the church where they have sought sanctuary and subsist on charity from the church, but in doing so are protected from arrest or actions of the civil authorities. It they leave, they are subject to arrest and deportation.
It worked when the Vandals sacked Rome, where it was rape or death not arrest and deportation: the Pope negotiated the inviolability of sanctuary and during the traditional three day sack of the city, those who sheltered in churches were spared, as were the churches. It worked all through the middle ages for those accuse of all manner of crimes. It will work just fine for those accused of violating our immigration laws.
(Who will want to sneak into the US if they know the only way they can stay is to become a charity case confined to a church?)
