I'm afraid I cannot see the connection, Bill, between God bringing Israel out of Egypt, and groups of people leaving European countries to settle in what is now the USA. There are so many differences. Here are a few:
1. Israel as a nation was in Egypt, away from their homeland, whereas the Europeans who settled in America left their original homelands. In this respect the settlers where more like Jacob & sons leaving Canaan to settle in Egypt.
2. It was the whole family of Jacob/nation of Israel in Egypt, but only a small percentage of the population of European countries left home for the "New World". Most of them, including some very godly Christians, stayed at home.
3. Israel was God's chosen nation in the Old Testament, but the European colonists who settled in America were not a nation, chosen by God or not.
4. God specifically commanded the Israelites, via Moses, to leave Egypt. Not so with the colonists.
The matter of how we treat fellow human beings regardless of their ethnic origin is surely better exemplified by the parable of the Good Samaritan.
Anyway, your theme is "illegal aliens" (here we tend to call them "illegal immigrants"). Far from Israel being "illegal aliens", Egypt wanted them to stay.