First, on your point about "private organizations", those "private" organizations represent an entire nation, so it's a bit different than having a church use arbitrary standards on who can worship in what is purely a private function.

Second, while I'm sure that some of the people opposed to immigration may be racists (including Voula Papachristou), the notion that nations are ethnic homelands (aside from the US, which pretty much wiped out its native inhabitants, Canada, which came close to doing the same thing, Australia, which came close to doing the same thing, etc.) is not necessarily a racist one. The reason the UN endorsed the establishment of a Jewish homeland in Palestine after World War II was in part because it was felt that if the Jews had a nation that was "theirs", it would be harder to repeat the Holocaust. I could rephrase that notion the way my father-in-law puts it: "I might move to Israel. Everywhere else there will be people who say I'm just another dirty Jew."

As a result, an influx of immigrants with different traditions and ways of living can be seen as a threat to this cultural link, particularly for smaller ethnic groups. I don't think that everyone who is anti-immigrant is by definition racist. Conservative, perhaps reactionary by definition, but not ipso facto racist. I'm not going to presume to know what is in the hearts of every person who wants to limit immigration in European countries.