Elsewhere, Ron Weber, a West Point graduate and lawyer in Ohio who beat three other contenders in a primary and has shared QAnon hashtags and conspiracy theories on social media, lost his race on Tuesday.
But it is Ms. Greene, the victorious candidate in Georgia, whose candidacy has exemplified the party’s difficulties in handling its QAnon problem. Now that she is headed to Congress, the party must decide what to do with her.
“I think she will start off with a pretty short leash,” Mr. Buck said.
Even so, he added, there is a fundamental problem: “There is no real establishment or party leadership in the way that there used to be,” and so “members of Congress have realized that there is an open playing field to be whoever you want if you can get attention for yourself.”
Ms. Greene, who owns a construction company, has called QAnon “a once-in-a-lifetime opportunity to take this global cabal of Satan-worshiping pedophiles out.” She has also made derogatory remarks about Black people, Jews and Muslims.
Nearly every elected Republican in Georgia’s 14th Congressional District, where Ms. Greene was running for an open House seat, lined up to oppose her after she trounced eight other candidates in the June primary and forced a runoff. But not everyone in the party was as unwelcoming. Mr. Trump posted a congratulatory tweet after Ms. Greene’s strong showing in June, and two of his highest-profile supporters backed her: Representative Jim Jordan of Ohio and Mark Meadows, the former congressman who is now the White House chief of staff.
Whatever objections others had seemed to melt away after Ms. Greene won the runoff in August. Representative Kevin McCarthy of California, the House minority leader, said she would be given committee assignments if elected. Senator Kelly Loeffler, who was appointed by the governor last December and is seeking a full term in a special election in Georgia, readily accepted Ms. Greene’s endorsement.
Ms. Greene, for her part, has recently sought to distance herself from her most controversial views. Asked about QAnon in an interview with Fox News, she said she had chosen another path. She also tweeted that she had now accepted that the Pentagon had been hit by a hijacked plane on Sept. 11, 2001, not a missile.