The Holy Office silenced Murray owing to his (false; heretical really) ideology of religious liberty.
«Four Erroneous Propositions»
It is now possible to identify the propositions censured by the Holy Office. In the Roman diary of Joseph Clifford Fenton and in the papers of Francis Connell can be found the following text:
PROPOSIZIONI DOTTRINALI ERRONEE
a) The Catholic confessional State, professing itself as such, is not an ideal to which organized political society is universally obliged.
b) Full religious liberty can be considered as a valid political ideal in a truly democratic State.
c) The State organized on a genuinely democratic basis must be considered to have done its duty when it has guaranteed the freedom of the Church by a general guarantee of liberty of religion.
d) It is true that Leo XIII has said: «(. ..) civitates C..) debent eum in colendo numine morem usurpare modumque quo coli se Deus ipse demonstravit velie» (Ene. Immortale Dei). Words such as these can be understood as referring to the State considered as organized on a basis other than that of the perfectly democratic State but to this latter strictly speaking are not applicable.
A convergence of arguments enables one to conclude that this set of censured propositions is in fact the text sent to Murray.
First, they are the work of the Holy Office. Fenton received them from Cicognani at the Apostolic delegation on October 28, 1954, and he immediately added: «Sicut in alia materia adfuit SOFTHO», which I take to mean: «As in the other material there was the Secret [or Seal] of the Holy Office». In Connell's papers the same text is found in an envelope on which is typed: «Under the seal of the Holy Office».
https://jakomonchak.files.wordpress.com/2014/06/jak-silencing-of-jc-murray.pdf
It appears to ABS that what The Holy Office silenced Murray for was what was produced by the progressives (Dignitatis Humanae) at The 60s Synod.