My theory is that at some point since Ronald Reagan, restricting immigration switched from being a liberal position to the conservative position. How should we test that theory?

There have been countries in the past, and the present, that are a liberal dream come true, and countries that have been a conservative dream come true.

Did the liberal dream countries have open borders or closed borders? The USSR, North Korea, Cuba, and the Eastern European satellite countries, all had closed borders.

The conservative dream countries, the U.S.A. at its founding (not minimizing the shameful history of slavery) had completely open borders until 1882.

So there you have it. Consistent liberalism means closed borders. Consistent conservatism means open borders.