Last year or the year before, William Barr gave a speech at (IIRC) Notre Dame where he told an interesting story.
He is a practicing Catholic, and found himself attending Mass at a church he hadn’t attended before.
As is frequently the case at Mass, after the ceremony itself was over, but before the congregation was formally dismissed by the priest, there was a brief period of announcements.
Barr told of how the chairman of the parish food committee (or something like that) went to the lectern and discussed the dire need in the community. Lots of people going hungry, etc.
What came next is what surprised him. His assumption was that the speaker would then say something “And therefore we are taking up a special collection now to help these hungry people”.
That didn’t happen. Instead the speaker talked about the committee’s efforts to petition the local city council for additional food relief money.
Which gets to my view on your immigration/health care question.
I think, beyond a doubt, that Christian charity requires individuals to disregard things like national borders. A person in need is a person in need.
But Christian charity is also, fundamentally, personal in nature. The idea that the demands of Christian charity can be met by petitioning “Caesar” to put a sword to your neighbor’s throat, take his money, and then give that money to the deserving poor is, in my view, abhorrent.
As an aside, I note the asymmetry we often see. If a Christian argues that the bible demands that gay marriage or abortion be prohibited, we are told that such a policy is prohibited by the First Amendment. But if we are told that Christian charity demands public welfare programs, no establishment clause objection is heard.