What does Catholicism have to do with "(American) conservative"?
Some beliefs of Catholic faith are agreeable to American "conservatives" - "homosexuality bad, no abortion, no euthanasia". Others are music to the ears of American "liberals" - "help the poor and downtrodden, love the foreigner and everyone else, no capital punishment". But the church is the church. I don't see it as liberal or conservative. I suspect if you asked the pope, or cardinals or bishops, most would say the church is beyond such secular concerns and labels.
It has been around for far longer than any political movement or country. And I'd bet good money that it outlasts all of them.
> pushing views
A religious leader espousing religious views? Shocker.
> strongly opposed to Catholicism
Literally wrong. Only the Pope can tell you what Catholicism is. You can take it or leave it but that's how it is.
So to add to what you're saying here, a pope cannot teach error in specific infallible declarations on faith and morals, because then the whole Church would fall in to error.
Ergo, some like St. Robert Bellarmine have argued for example if a pope were to teach heresy, he would immediately cease to be a pope; others have argued it impossible for a pope to ever teach heresy at all as this was something they believed God wouldn't allow.
So, if you were to see someone claiming to be pope and teaching error on infallible issues of faith and morals, you'd have to conclude logically they could not be a Catholic pope, from a Catholic standpoint.
> [the pope] poses as "conservative" while pushing views strongly opposed to Catholicism."
is a nonsense statement.
The Pope is Catholic and he preaches Catholicism. The Pope doesn't "pose" as anything. Some of what he preaches sounds conservative or liberal or whatever. That doesn't matter to him. What he promulgates was already ancient when any political movement of today was born.
> "the pope [appears to be] pushing views strongly opposed to Catholicism"
According to who? It's a safe bet that a pope won't say "actually now you may covet your neighbor's wife" without a head injury or dementia being involved (in which case his staff would cover for him or he'd be retired somehow). That leaves questions of arcane doctrine that a regular Catholic simply isn't qualified to judge. They have the choice of leaving the church or staying and obeying as best they can.
While the Vatican does have walls, anyone can pretty much just walk on through them with perhaps a trip through a metal detector, so not sure what you mean.
The Catholic Church also does not teach that there cannot be restrictions on immigration, it simply says that we should treat people with dignity while enforcing such restrictions.
Neither Francis nor Leo (not sure which you mean by New Pope) have stated deportations or restrictions on immigration are wrong. Unfortunately, they are often taken out of context or do not provide clear statements which leads to confusion like you are experiencing.