“Immigration is a kind of proxy war — and maybe a last stand — for White Americans, who are undergoing a painful recognition that, unless dramatic action is taken, their grandchildren will live in a country that is alien and hostile,” Mr. Spencer wrote in a National Policy Institute column.

Infowars is another website that puts immigration front and center. The site was created by the radio commentator/conspiracy theorist Alex Jones, who is the source of Mr. Trump’s false claim that thousands of New Jersey Muslims celebrated 9/11, and on whose show Mr. Trump said: “Your reputation is amazing. I will not let you down.” Infowars called Mr. Trump’s slashing anti-immigrant rant on Wednesday “an excellent speech sure to win him support from those who’ve been conned by the lying media into thinking he’s some evil demon creature when the truth is he’s a man with a heart of gold.”

Mr. Trump says he isn’t signaling the alt-right when he says of immigrants, as he did again on Wednesday: “We have no idea who these people are, where they come from. I always say Trojan Horse. Watch what’s going to happen, folks. It’s not going to be pretty.” Or when he said — in a line widely quoted on alt-right websites — “There is only one core issue in the immigration debate and it is this: the well-being of the American people.” Mr. Trump’s white supremacist followers don’t take his disavowals too seriously. After all, he has enthusiastically retweeted bogus crime statistics and incendiary imagery from these websites and hired one of their biggest lights, Stephen Bannon of Breitbart News, to manage his campaign.

There aren’t enough of these people to put Mr. Trump in the White House. But his candidacy has granted them the legitimacy they have craved for years. For the first time, a candidate is using a major-party megaphone to shout the ideas they once could only mutter among themselves in the shadowy fringes of national debate.