Steve Chapman, writing in a reposted 2007 article at Reason, explains Why the Right Shifted on Immigration.
Chapman thinks the shift began with the fall of the Berlin Wall, when many conservatives no longer saw immigrants trying to reach our shores as proof of America’s sound economy and society.
If so, consider the cynicism of the Right: they didn’t support individual liberty for its own sake, but as a talking point in an ideological battle with the Soviet Union.
Broad-based free markets in capital, labor, and goods are superior in efficiency and morality to their alternatives. They didn’t become less so because the Cold War ended.
Then or now, a free flow of labor benefits America. Conservatives will have none of it today.
Libertarians might, of course, decide that a battle with the Left requires support for conservative candidates who back immigration restrictions, however Draconian. Those libertarians may choose as they wish, but they would do the liberty-movement a courtesy if they were to call themselves by another name.
Conservative, I think, would fit nicely.
The rest of us will do better to stay as we are, advocating for individual liberty, limited government, free markets in capital, labor, and goods, and peace abroad.