Western nations have democratic processes which allow for the rule of the people by the people. However when you let millions of non-assimilated peoples into your lands what do you think will happen? The balance of power can shift. You are kidding yourself if you think that it can't. Its a simple numbers game.
Go back to your history books. We're not far removed from when kingdoms were focused on growing numbers in order to wage war/dominate their areas..
Reminds me of a quote from founder and first Chief Justice and abolitionist John Jay (below). Many modern people have almost no understanding of human nature - behavior is all "chemicals" to them. They also have worse than no understanding of history - having thoroughly imbibed Marxist history slicked into education (raise your hand if you think "everyone is special").
“With equal pleasure I have as often taken notice that Providence has been pleased to give this one connected country to one united people — a people descended from the same ancestors, speaking the same language, professing the same religion, attached to the same principles of government, very similar in their manners and customs, and who, by their joint counsels, arms, and efforts, fighting side by side throughout a long and bloody war, have nobly established general liberty and independence.
This country and this people seem to have been made for each other, and it appears as if it was the design of Providence, that an inheritance so proper and convenient for a band of brethren, united to each other by the strongest ties, should never be split into a number of unsocial, jealous, and alien sovereignties.”
John Jay