Four-time Olympic medallist Louis Smith has been suspended for two months by British Gymnastics over a video in which he appeared to mock Islam.
Smith, who won pommel horse silver at Rio 2016, later said he was "deeply sorry" for his "thoughtless actions".
Carson was given a reprimand.
Smith, 27, is one of Britain's best known gymnasts and won the BBC show Strictly Come Dancing in 2012.
"It is regrettable that following a historic summer of achievement, the organisation finds itself in this difficult position with two high-profile members in breach of our standards of conduct," British Gymnastics chief executive Jane Allen said.
"As the custodians of the integrity and values of the sport, we have had no choice but to act responsibly.
"Whilst both individuals showed remorse following the incident, we hope in the future they use their profile to have a positive impact on sport and communities."
British Gymnastics said Smith's ban was a "cumulative penalty" because of a previous breach of its rules on conduct.
He was reprimanded in June for posting an image on social media of an American gymnast, who was 16 when the photograph was taken, accompanied by a comment British Gymnastics said was "unbefitting to a participant".
In April, he apologised for questioning the judging at the British Championships, where he was beaten to pommel gold by Max Whitlock.
The Briton missed last month's Olympic and Paralympic celebrations for Britain's Rio 2016 medallists to visit two London mosques "to learn more about the Muslim community".
Smith said he had previously been "ignorant to people's religion" and added on Facebook that it was his responsibility "as someone of sporting influence" to exercise freedom of speech "in good taste".
Carson's reprimand will stay on his record for two years, but the 27-year-old is still able to coach.
Smith is taking a break from the sport and is touring as a guest celebrity on the Keep Dancing stage production.
BBC News.
