Thomas Mann was raised in the Protestant, Lutheran faith, and in American exile he drew close to the Unitarian Church. The sources do not allow his personal faith to be summed up in a word.
His mother was Catholic, but he was baptized in his father's Lutheran faith, according to the English-language Wikipedia, and the Historical Dictionary of Switzerland records his confession as Protestant. His wife, Katia Pringsheim, came from a secular Jewish family and later joined the Lutheran Church.
In California, during exile, Mann became close to the Unitarians, who helped relatives of his flee Europe. According to an excerpt from Heinrich Detering's book on the subject, Pastor Ernest Caldecott, of the First Unitarian Church of Los Angeles, baptized his grandchildren Frido and Angelica in April 1942; the same excerpt says that a Unitarian pastor conducted the funeral of Thomas's brother, Heinrich Mann, as Thomas wished, without naming the pastor. The German-language Wikipedia says that Mann even joined the American Unitarians, whom he appreciated for being a community of faith without dogmatic foundations.
These data show the confession of origin and a closeness to Unitarianism; only the German-language Wikipedia speaks of membership. The Detering excerpt does not say whether there was formal membership in any church, and the English-language Wikipedia records only the Lutheran baptism.