Redemptorist Fr. Gerry Moloney told NCR "something is rotten in the state of the CDF, and while the current people and processes remain in place, nothing will change."
Analysis: The pope may have exposed church tensions over how to engage the gay community -- tensions that have intensified after the Orlando mass shooting at a gay nightclub.
German Cardinal Reinhard Marx also told NCR that Pope Francis' Vatican reforms depend on "a new relationship between lay people and clerics, that is clear."
Archbishop Diarmuid Martin confirmed that Pope Francis, or his successor, will visit Ireland in 2018 for the World Meeting of Families.
One of the issues that is likely to be to the fore in Ireland's general election, slated for Feb. 26, is the future of denominational education. The Labour Party has pledged to end the "baptism barrier" to school entry if re-elected.
The Association of Catholic Priests in Ireland is to write to the Vatican's Congregation for Bishops expressing its members' "grave disquiet" over the current selection process for Irish bishops.
Augustinian Fr. Gabriel Daly said that the 1968 papal encyclical had never been accepted by the church at large. Daly also condemned the church over its treatment of women.
"Throughout the debate and the discussion, we did ask people to try to be respectful and inoffensive in language," Archbishop Eamon Martin said.
Catholic Ireland has become the first country to introduce gay marriage by popular vote, with 62 percent voting "Yes" in a referendum on Friday.
Archbishop Diarmuid Martin of Dublin said he would seek assurances from religious congregations operating in his diocese that they are rigidly following child protection guidelines after a fresh round of audits raised serious concerns.
In a statement Tuesday, Martin said it was "appalling" that some major religious congregations had delayed fully implementing the church's child protection guidelines and that, in some cases, this process only really got underway in 2013.
Martin said the delays left him "seriously concerned."