Democrats have tolerated it.
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George W. Bush claimed to be a Republican and he tolerated it, too.
Actually, Bill Clinton was pretty good about enforcing the border, at least here in Southern California. I remember when B.J. was president Border Patrol agents always boarded the Amtrak train in Capistrano and they always arrested illegals on the train. That stopped when Bush became president.
W encouraged it, way beyond just tolerating it. He pushed for amnesty and only the patriots in the house at that time stopped it. I don’t think the current house would do so.