In an article by Father Richard P. McBrien called The lessons of Pope Cornelius.
There is a lesson to be learned, even today, from Pope Cornelius’s pastoral style. He reigned at a time of controversy and internal conflict in the church, which has proved to be all too common throughout its history and into our own time.
The issue then was whether those who had been baptized by heretics or by schismatics (those who had broken communion with the church but without denying any of its doctrines) were required to be rebaptized upon entering or returning to the Catholic Church.
On one side were those, including Cornelius, who favored a pastorally compassionate approach. Rebaptism should not be required. An act of contrition and some sign of repentance were deemed sufficient.
How is not having a rebaptism a pastoral approach. Scripture clearly speaks of one faith, one baptism – and not rebaptism is not a pastoral action but in fact a theological one. This was not a pastorally compassionate approach but a position consistent with the faith of the Church.
He goes on to talk about the "rigorist" Novatian who I guess from the context of the article is suppose to parallel Catholic conservatives today
Because of Novatian’s persistent and divisive opposition, Cornelius excommunicated him and his followers, but not on his own authority alone. He convened a synod that was attended by 60 bishops and many priests and deacons. The synod supported the excommunications and also the pope’s policy of readmitting to full communion, after appropriate contrition and "the medicines of repentance," those who had lapsed during the Decian persecution.
Cornelius sent copies of the synodal decisions to various bishops, including the rigorist, pro-Novatian bishop of Antioch in order to persuade him to end his support for Novatian and to accept the pastorally moderate approach adopted by the majority of churches.
In the very unlikely event that the Holy Father called such a synod today to excommunicate known heretics I wonder just how long after that that Fr. McBrien would be calling this compassionate pastoral action? When the majority of his companions at the National Catholic Reporter were excommunicated for their undeniable false teachings (I can dream can’t I). I think the lessons to be learned by Pope Cornelius are not the lesson that Fr. McBrien would have us learn. That a Pope at times needs to act to eliminate false teachings and pastoral action action does not always mean with approval of all the Bishops. In this case the majority of Bishops were against Novatian and the Pope wrote multiple letters to the Bishop of Antioch who was wavering in his support. This Pope held firm to the faith though he was later exiled and died a martyr.