“For the Jews were offered three opportunities of peaceful relations with foreigners. First, when foreigners passed through their land as travelers. Secondly, when they came to dwell in their land as newcomers. And in both these respects the Law made kind provision in its precepts: for it is written (Exodus 22:21): ‘Thou shalt not molest a stranger [advenam]’; and again (Exodus 22:9): ‘Thou shalt not molest a stranger [peregrino].’”That's immigration law. Anyone can immigrate in, and no one can be molested when they do. He's fine with open borders.
But, for naturalizing the immigrants (giving them the right to vote and hold office), he, as well as the founders of the US, recognized the standards would have to be higher.
“Thirdly, when any foreigners wished to be admitted entirely to their fellowship and mode of worship. With regard to these a certain order was observed. For they were not at once admitted to citizenship: just as it was law with some nations that no one was deemed a citizen except after two or three generations, as the Philosopher says (Polit. iii, 1).”So, yes, Aquinas was fine with open borders, but he insisted on tight naturalization controls.
“The reason for this was that if foreigners were allowed to meddle with the affairs of a nation as soon as they settled down in its midst, many dangers might occur, since the foreigners not yet having the common good firmly at heart might attempt something hurtful to the people.”This is absolutely identical to US policy for the first century of its existence: anyone can come in and make a life for themselves here, without needing any papers, passports, etc. But if you want to vote and hold office in this country, you are held to stringent naturalization requirements.
So, any conservative who insists on Original Intent (tm) has to be fine with open borders, because that was the Founders' original intent. And, the Founders' original intent was completely in conformance with Thomistic principles, so it's not like a Catholic has any real grounds to object.