They compare this national home to a private homeowner's right to keep people from entering his home.

But America is not a national home. Immigration-control advocates who make this argument to justify their immigration scheme are thinking of countries like Cuba and North Korea. In those countries, the government owns everything and considers the entire country to be its property. Thus, the national-home argument is a better fit for nations that are based on collective state ownership of everything. 

But the United States has always been based on the concept of private property. Sure, the federal and state governments own a lot of land. Nonetheless, the nation is still based on the concept of private ownership of property.

A private owner has the right to decide who enters his house or business. And it doesn't matter what his reasoning happens to be. His authority to prevent others from entering onto his property is complete, even if it is based on the most prejudicial of reasons. Thus, if a private owner decides, for whatever reason, that he doesn't want immigrants to come into his house or  his business, that is his moral right, even if everyone else disagrees with it. As the old saying goes, a man's home is his castle. And so is his business.

By the same token, a private owner has the right to permit anyone he wants to enter his house or his business. That includes immigrants. If I wish to invite immigrants into my house or my business, that is my right. No one else has the right to prevent me from doing so.