Population growth is inevitable, whether by the native population or by immigrants. To advocate otherwise is to be a eugenicist or a racist. You can’t stop it but you can control the flow to suit society’s needs.
You have misused the word eugenicist, in a way which makes me wonder if you ever read any of Sir Francis Galton's work. But then, when you call people "racist," who merely desire to maintain the ethnic character of their States and communities, you cross a line, which suggests that you are not interested in a civil exchange of ideas. Slurs are for propagandists, who cannot answer rational argument.
As for population growth? I suggest that you look at the native populations of much of Europe today. Or contrast Medieval Europe with Roman Europe. And, indeed, if we are going to have native population growth, that is all the more compelling reason--given the present nunmbers--to stop the influx over the border.
William Flax