I must be clear, I have always struggled with the Roman teaching on Papal Infallibility. Having said that, I also know that it does not mean what most (ignorant) folks, whether supportive or critical, think it means. It does NOT mean that the Pope cannot make a mistake. It does not mean that every word he speaks is inspired Scripture. It does not mean that he is flawless and errorless. Rather, it is a claim that when the pope declares, ex cathdra- from the chair, something to be authoritatively true (like the Immaculate Conception or Assumption) that the declaration has the same warrant for belief as Scripture. [In fairness, I find the typical Protestant case for "inerrant" Scriptures to be equally overstated and overly simplistic. It seems that one temptation of religion is to find something to cling to which saves us from the uncertainties of life; something more concrete than an absolute trust in God...]
My theological difficulties with the teaching on the papacy led in no small part to my eventual demise as a Roman Catholic. However, years later as a member of a more "democratic" church with a "looser" approach to authority and church, I am less enamored with the alternative to Roman Catholicism's hierarchy. I have learned the bitter lesson that if the (ancient) belief in rule by a "nobles" class is fraught with abuse, the sad fact is the masses are likely to be driven by the same petty self concerns. People who can vote (in conventions) on morality and beliefs vote with a self interest which easily ignores the Truth. In the Gospel, Jesus was executed by the ruling classes (both Jews and Romans), but we are reminded that the crowds cried out "Crucify Him!" Life before the Kingdom Comes is always going to be tainted by sin.
So why should "other" Christians care what man is chosen to wear the white robes and beanie?
Traditional Christians should care because the Papacy, especially in recent years, has been our loudest advocate. The Pope's stand on tradtional faith has consistently been the best articulated and firmest example of Christian beliefs world-wide. He may be mocked but he is not ignored. Even if ignored, he impacts millions in our own country through the (admittedly muted) local dioceses and parishes. Probably the "progressive" types should care because the Church of Rome, for all her practical faults and failures, has been the one institution to stand against its heresies. Evangelical pastors speak out as well, but it is their assumption that the church is individuals and local. As such, Evangelical pastors can only speak for, even in very large churches, at most a few thousand folks, but usually fewer than two hundred. Evangelical churches are easily ignored. The University of Memphis basketball team has a larger following and larger public gatherings then any one church in West Tennesse (though that is not true of the Roman Catholic diocese of West Tennessee). Rome is the bane of Progressives. It is public enemy number one and the reason they "hate" the Catholics is because the Catholic voice (against abortion, gay marriage, etc.) is the loudest and most consistent against the progressive agenda. Anti-Christ (in the broader sense) has Rome in its target. This is why so much media attention is focused on the sins of the Roman church. (Question, are Catholic priests the sole source of sex abuse? In the media they are, in fact they are not.)
For all my issues with Roman Catholic ecclesiology, I still recognize the Bishop of Rome as the central figure of Western Christendom. I believe that whoever sits in the Chair of Peter has greater import than any other religious leader in the world. Famous preachers inspire, a Pope also rules. Human institutions, even if under Divine guidance, always have humans in charge. Be it Main Street Bible Church, Fourth Presbyterian, or Holy Fire Pentecostal the local congregation, even if prayerful, Bible based and faithful, is always under control of human agents (who interpret God as they see fit). When a person is in charge of a church with a billion members (even though many are non-compliant and nominal) he necessarily has greater influence.
I stand against Rome on some counts, but with Her on many more. I am praying for a good pope. I am hoping for a man who will stand against the evils of our world, who will reform his church and postively impact all churches. I pray he will stand for the faith and for the truth. I know the candidates are amazingly brilliant, experienced and gifted (though flawed) human beings. I still wonder if anyone is up to the task. I do note envy whoever is elected. I just know he will matter greatly. And in these days of greater darkness I suspect he will feel greater heat from the Satanicly influenced world, inside and outside the church. The pope matters. Even for us who live outside his jurisdiction.