These activists cheered when Mr. Trump suggested that the Jewish billionaire George Soros could be secretly funding a caravan of Latin American migrants — a dog-whistle reference to an anti-Semitic conspiracy theory that has been advanced by neo-Nazis and white nationalists for years. They roared their approval when Mr. Trump began stirring up fears of angry, violent left-wing mobs, another far-right boogeyman. And they have found traces of their ideas in Mr. Trump’s rhetoric, including his concern for an obscure land rights conflict involving white farmers in South Africa and his references to asylum-seeking migrants as “invaders.”

“Most of these conspiracies are not new to us,” said Oren Segal, the director of the Anti-Defamation League’s Center on Extremism. “I’ve seen white supremacists and extremists talk about these anti-Semitic and racist ideas for years. But it was always in the corner. Now, you don’t know where the mainstream starts and the fringe ends.”

Since the 2016 election, these far-right communities have entered into a sort of imagined dialogue with the president. They create and disseminate slogans and graphics, and celebrate when they show up in Mr. Trump’s Twitter feed days or weeks later. They carefully dissect his statements, looking for hints of their influence. And when they find those clues, they take them as evidence that Mr. Trump is “/ourguy/,” a label for people internet extremists believe share their views, but who are unable to say so directly in public.