Stephen Bannon, President Trump’s brain, was the biggest draw of opening day at the Conservative Political Action Conference, Washington’s annual gathering of the Republican right. After his standing ovation on Thursday, the White House chief strategist couldn’t resist reminding assembled conservatives that until he helped them win the presidency, he and his fellow alt-right believers weren’t welcome.

With a smirk, he told Matt Schlapp, chairman of the American Conservative Union, “I want to thank you for finally inviting me to CPAC,” and Mr. Schlapp hastened to assure him that “we decided to say that everybody’s a part of our conservative family.”

If that’s true, then what does it mean to be part of this “conservative family”? Traditional conservative leaders face questions that can’t be solved — and may be compounded — by saluting the previously “uninvited” at their signature conference. Do they embrace Mr. Trump, who created the best opportunity in a generation for passing a conservative agenda by wooing bigots, bomb-throwers and reactionaries? Or reject them, and risk irrelevancy?

At its founding four decades ago, CPAC was a sleepy, libertarian-leaning gathering, heavy on college Republicans, professors and policy. Conservative intellectuals led by William F. Buckley Jr. long ago rejected having fringe elements like the John Birch Society in the fold. Today, the Trumpian uninviteds are ascendant, and their power and celebrity seem irresistible to the next wave of Republicans. Breitbart is now a conference sponsor; the booths of alt-right radio conspiracy outlets line the hallway.