Rod Dreher quotes Peter Hitchens  as noting, “lax immigration politics … have revolutionised the country and will render it unrecognisable within 30 years.” It’s already unrecognizable, depending on where one sets the benchmark: a 19th century American would be surprised to see a majority Catholic, minority Jewish Supreme Court, as we have today, along with presidential tickets consisting of a black man and a Catholic and a Mormon and a Catholic. More than just immigration is responsible for this, though immigration certainly amplified the Catholic presence in American life. The U.S. today is still majority white, which it won’t be in 30 years time, but it’s already an America vastly different, ethnically and religiously, from that of a century ago.
Thomas Jefferson already didn’t recognize the country that leaned toward Andrew Jackson in 1824  and was gripped by the religious enthusiasm of the Second Great Awakening. As Gordon Wood has remarked :
He disliked the growth of the North which he thought was a hotbed of Federalist bigotry and religious enthusiasm mingled with Yankee money-making. That Andrew Jackson almost became president in 1824 appalled him. He thought Jackson was a primitive, violent man unfit for the presidency. All in all he thought the country was going to hell in a hand-basket.
Wood’s book Revolutionary Characters  brilliantly shows how political and class changes after the American revolution led to a country completely transformed from the aristocratic colonial America that had shaped the Founding Fathers. That’s the point, of course, of the classic tale of Rip van Winkle , too.
There are two things to keep in mind in all of this. The first is that these changes in national character do not mean the destruction of the country or of all virtue. The second is that these changes were indeed profound and did involve loss and alienation for those who remembered the old order.
Change in the social order is momentous; some things are preserved, albeit in a transfigured way, and some things vanish. There’s no use trying to deny or prevent all of this: the conservative’s task is to preserve something, not everything. The fundamental thing to be preserved is order itself, and preserving order in a changing society — changing politically, economically, religiously, and ethnically — requires that order be dynamic rather than nostalgic. Edmund Burke understood this very well. As he said in what he hoped would be his last word on the French revolution :
The evil is stated in my opinion as it exists. The remedy must be where power, wisdom and information, I hope are more united with good intentions than they can be with me. I have done with this subject, I believe for ever. It has given me many anxious moments for the two last years. If a great change is to be made in human affairs, the minds of men will be fitted to it; the general opinions and feelings will draw that way. Every fear, every hope, will forward it; and then they who persist in opposing this mighty current in human affairs, will appear rather to resist the decrees of Providence itself, than the mere designs of men. They will not be resolute and firm, but perverse and obstinate.