Why did the GOP do so well in early 20th, late 19thc despite massive immigration

[Southern Senator North Carolina Yankee]

The areas where immigrants are in large numbers, is where you see the immigrant backlash. It is also worth remembering that these states overall were majority Protestant even as late as the 1920s. This means that you have the immigrants there to motivate high Republican vote margins among the assimilated demographics, while said group still has enough numbers to dominate the area. The best analogue for what happened in say Massachusetts in the early to mid 20th Century, is SoCal in the past twenty years.

Eventually you reach a point when the math no longer works obviously.