After Hurricane Helene, Representative Marjorie Taylor Greene, the hard-right conservative from Georgia, shared on X the widely debunked claim that government scientists could control the weather. “It’s ridiculous for anyone to lie and say it can’t be done,” she wrote in one post.

The conspiracy theorist Alex Jones repeatedly posted on X erroneous claims about Hurricanes Helene and Milton, including that the Pentagon had somehow engineered the storms.

“Treason Alert,” Mr. Jones wrote in one post. “America is the target,” he warned in another.

In just those three posts, Ms. Greene and Mr. Jones racked up a combined 72,000 likes, and over 34,000 shares. They are only a handful of the many misleading diatribes and conspiracy theories that regularly appear on X.

Not long ago, those two would not have been able to publish those posts through their accounts.

Ms. Greene and Mr. Jones are among a large set of users who were barred from the site for spreading misinformation, inciting violence or otherwise violating its rules — and were reinstated after Elon Musk bought the platform, then known as Twitter, two years ago.

Many of these people picked up where they left off, according to a New York Times analysis of 50,000 posts by more than 100 high-profile reinstated users. They include Laura Loomer, a right-wing influencer who has campaigned with Mr. Trump; Mike Lindell, the chief executive of MyPillow; and Rogan O’Handley, a right-wing political commentator. All have a broad reach — at least 100,000 followers — and were identified by researchers who study disinformation or extremism on X.

Most hold right-wing or even far-right views, and are part of a broader political shift underway on X. With just weeks before the U.S. election, Democrats have been abandoning the platform, according to recent academic research, while use by Republicans has remained steady. After publicly endorsing Mr. Trump for president in July, Mr. Musk has used X as a bullhorn to promote the candidate, one that many of the reinstated accounts then echo.