The Republicans were historically the party that was pro-immigration. They wanted more H1 and H2 visas to keep costs down. It was Reagan who granted Amnesty to millions of illegals in the 80s. (I-9s were supposed to limit the demand for future illegal immigration back in 1986, but have not been an effective deterant.)
Democrats in the 80s beholden to organized labor, fought to limit immigration to keep unskilled and semiskilled wages high. Some unions still hold this view, but others seem immigrants as their primary opportunity for growth so this is shifting.
This whole Republicans oppose immigration and Democratics favor it is a relatively new phenomenon over the past 20 years.
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