Conservatives by default hold the middle ground position. Conservatives aren’t against immigration despite what the Left say. Conservatives is just against illegal immigration
I think a better way to say it is, yes, conservatives favor legal immigration, but not Lyndon Johnson's political immigration, which he intended would swamp America with socialist, reflexively 'Rat-voting Mexicans who generally dislike America to begin with, and, like the Castro brothers and their white-hating racist mother and the election-stealing Sanchez sisters who cheated "B-1 Bob" Dornan in California by running illegal Mexicans into the polls, love racist machine politics.
Is that a "more nuanced position"? Ted can steal that one.