Legal immigrants fleeing Communist, Muslim or Tatmadaw repression in Asia (or Africa), immigrants from places where Anglo-Saxon legal norms were established for over a century (e.g. India, Nigeria, Ghana, Jamaica), and immigrants from democratic capitalist countries in East Asia (Japan, S. Korea and Taiwan) should all be as welcomed as immigrants from Europe.
The real problems come from Muslims and criminal elements among Latin American immigrants.
Personally, I'm hoping we get enough immigrants from India that we can become a serious contender in a sport which was beloved of Benjamin Franklin and Abraham Lincoln, but despite its popularity in the rest of the Anglosphere has fallen into disregard in the United States -- cricket -- I'd love to see the United States fielding a test cricket team, we're already doing well in the one-day formats of the game.