I don't blame the immigrants at all, I blame our government (who is supposed to serve us) for not protecting us from them. I also believe in ethnic/cultural cohesion, it's ok to migrate, but it usually happens during periods of crisis, not as a positive good.
God made "peoples" (ethnicities), and Israel had divinely inspired borders. At the same time, God was also the one who drove Nebuchadnezzar to conquer the entire known world, dissolving those borders and re-organizing everything. And yet there are still people who trace their lineage to places as specific as Syria and Chaldea.