This is similar to the topic of, should Catholic Christians attend a same-sext “marriage.” I have a suspicion that you would say that there is no problem with this.
Dr. Taylor Marshall would probably fit in your second category. He has been very critical of Pope Leo and other Catholic Bishops hosting this Lesbian Pastor. Dr. Taylor was once an Anglican Priest before converting to the Catholic Christian Church.
If you read the writings of the Early Church Councils, they were very critical of heretics.
We know that there are some in the Church who want so badly to pervert the Faith. They look at the Archbishop of Canterbury as a step in the right direction, in which, I say, if you believe this, then you should go be Anglican or ELC Lutheran. There is the Church for you. Don’t try and make the One, Holy, Catholic, and Apostolic Church more Protestant.
The Eastern Orthodox Church is pretty good at protecting orthodoxy (maybe, because it is in their name). And the more that the Catholic Christian Church fails to protect orthodoxy in the name of ecumenicalism, the more appealing the Orthodox Church becomes.
When we say that the Apostolic Church (Catholic/Orthodox) is universal, we mean that it is for all nations, and encompasses the fullness of faith. But, some hear this word and think that it means that the Church should water-down her teachings so much that it includes and does not offend anyone. A sort of unitarian view of the Church rather than a Church that is katholikos. This is what I mean by a perversion of the Faith.
If you believe the Church should become less catholic and less orthodox, then you should go join a Unitarian Church. No hard feelings. I have given here three options for those who want the Catholic/Orthodox Church to “get with the times”: Universalism, ELC Lutheranism, Anglicanism, or go plant your own Church (that seems to be pretty popular these days as well among non-Denominationalists, of which I used to belong, before coming back to my Catholic Faith, only to find her engaging in metaphorical orgies with the neighbors, but I digress).
Can the Pope be friendly towards leaders of other Faiths, yes. John Paul II was friends with Billy Graham. Benedict was friendly towards some of the Eastern Patriarchs. I have no problem with this.
What I do have a problem with is when Catholic Bishops demonize Traditional Catholic Christians while elevating and going out of their way to be charitable towards individuals who pervert Historical Christianity.
We should demand more from our Bishops and Priests when it comes to their role of protecting the Apostolic Faith, which has been entrusted to and passed on to them.
This probably puts me in the second category. If I wanted a fluffy Church, I would have remained non-Denominational. They are “seeker-friendly” and lacked substance. It didn’t dare speak say anything that might offend someone. The truth is, Jesus would often offend others by speaking truth. Yes, He was more gentle if He was encountering someone who doesn’t know better, but our Bishops and Priests, should know better. And that is the problem.