It's also important to consider that the US, prior to the modern era, was a "melting pot" of a somewhat select group of immigrants. We routinely turned away handicapped, poor, sick, mentally deficient, or otherwise "unfit" potential citizens.

The "New Colossus" that adorns the Statue of Liberty is a fun little poem, but it does not in any way reflect the actual policies of the United States for much of its early and middle existence. We were a country that was happy to import wealthy people, scientists, conscientious hard workers, etc, while keeping the riffraff out.