WASHINGTON — As the Republican Party censures, condemns and seeks to purge leaders who aren’t in lock step with Donald J. Trump, Adam Kinzinger, the six-term Illinois congressman, stands as enemy No. 1 — unwelcome not just in his party but also in his own family, some of whom recently disowned him.

Two days after Mr. Kinzinger called for removing Mr. Trump from office following the Jan. 6 riot at the Capitol, 11 members of his family sent him a handwritten two-page letter, saying he was in cahoots with “the devil’s army” for making a public break with the president.

“Oh my, what a disappointment you are to us and to God!” they wrote. “You have embarrassed the Kinzinger family name!”

The author of the letter was Karen Otto, Mr. Kinzinger’s cousin, who paid $7 to send it by certified mail to Mr. Kinzinger’s father — to make sure the congressman would see it, which he did. She also sent copies to Republicans across Illinois, including other members of the state’s congressional delegation.

“I wanted Adam to be shunned,” she said in an interview.

His anti-Trump stance has angered Republican constituents in his district, some of whom liken him to a Democrat, and frustrated Republican officials in Illinois who say he cares more about his own national exposure than his relationship with them.

“There doesn’t seem to be a camera or a microphone he won’t run to,” said Larry Smith, the chairman of the La Salle County G.O.P., which censured Mr. Kinzinger last month. “He used to talk to us back in the good old days.”

Mr. Kinzinger is unapologetic about his priorities.