Religion

In 2012, Survivors Network for those Abused by Priests criticized Müller's appointment to the CDF because he had reinstated Peter Kramer in parish ministry after Kramer was convicted in 2000 of sexually abusing children. Kramer had completed court-ordered therapy. Müller did not inform those in Kramer's new parish of his past history. Müller had apologized in 2007 for mishandling the case.

In 2016, Fritz Wallner, a former chair of the lay diocesan council in Regensburg, Germany, alleged that Müller as Bishop of Regensburg had "systematically" thwarted the investigation of abuse in the "Regensburger Domspatzen" boys' choir. Georg Ratzinger, Pope Benedict XVI's brother, led the choir from 1964 to 1994. Müller insisted that neither the church nor its bishops were responsible for abusers. In February 2012, he said that "if a schoolteacher abuses a child, it is not the school nor the Ministry of Education that are to blame." He maintained that only the perpetrator is guilty. In 2016, a commission of 12 members was instituted to address the history of abuse and its cover-up in the boys' choir, a move critics viewed as long overdue. Wallner called for the church to purge any person associated with Müller, who had overseen the church's response to the allegations. In July 2017, a comprehensive report commissioned by the Diocese of Regensburg on abuse at the boys choirs said that Müller had "clear responsibility for the strategic, organizational and communicative weaknesses" of the church's response when the abuses were first reported.

Müller is being sued in France along with Cardinal Philippe Barbarin, Archbishop of Lyon, for failure to act in a case of sexual abuse of minors by a priest.