I spend a significant amount of time explaining Roman Catholic beliefs to my evangelical and Protestant friends. As a theologian it is part of my calling to illuminate and clarify. So much of what non-Catholics say about Catholicism is intended to obscure.
I also think it is a profoundly eschatological act to work for the unity of the church. Put another way: Jesus prayed for the unity of the church (John 17) and I believe his prayer will come to fruition in the New Heavens and New Earth. In the meantime, we pray and work toward a unity that will likely not be achieved until he returns.
But there are still some significant reasons why I don’t think the Protestant churches can reunite with the Catholic Church. Clarity about those differences are also important. So consider this a Protestant guide to understanding the Catholic Church.
All the talk of Catholics believing that salvation comes from anything but Jesus is dead wrong. Sometimes Protestants talk like Catholics believe that the rituals of the Church have some kind of salvific power on their own. Catholics believe that the sacramental system is the way that God has given to meet Jesus. Most Protestants would not believe that as strongly as Catholics.
But I suspect that many Protestants that are most prone to criticize Catholics have led someone in a “sinner’s prayer” and told them that this somehow assured their salvation. That is an infinitely more heretical position than any Catholic notion of the efficacy of the sacraments. At least since Vatican II and in most places long before that, the Catholic Church has insisted that the sacraments are dependent upon faithful reception of them. That means that the Catholic Church agrees that the sacraments only “work” in the life of the believer to the extent that they are received by a faithful heart. I would encourage any Protestants that are concerned about whether Catholics are sufficiently dependent upon Jesus to read The Joint Declaration on the Doctrine of Justification that was written by the Lutherans and Catholics.
That said, there are a few problems worth quibbling over. Catholic theology regarding Mary is problematic from a Protestant perspective. Catholics regard Mary as the first Christian, having said “Yes” to Jesus even as he is conceived. This isn’t problematic. But some Catholic theologians (though is not official dogma) call Mary Co-Redemptrix. Christ is still the one who gives grace to sinners in this thinking, but Mary’s obedience to God is somehow involved in making salvation possible by her receiving Jesus. Co-Redemptrix is a fringe theology among Catholics but it points to a variety of ways that Mary is given authority in the economy of salvation that Protestants will reject. Similarly, though official theology is such that prayers to Mary and the saints are only asking them to pray for you to God, even the Popes sometimes ask Mary to do things that only God can do.
The practice of intercession whereby a Catholic asks a saint (or Mary) to offer prayers on their behalf is not an issue that is ultimate. That is, it is a difference between Catholics and Protestants but it is not a matter of salvation or heresy. Catholics are simply asking deceased Christians to pray for them.
Some Protestants claim that the Pope is considered equal to the Bible in Catholic teaching. This is just an issue of different categories obscuring the truth. Catholics too believe in the final authority of Scripture. But that notion is configured differently for them. Catholics give authority to the whole Tradition of the Church’s apostolic teaching, of which the Bible is the key piece. They would say that the Bible, the teaching of the Popes (not everything a pope says, but when he is specifically acting as “pope”), the liturgy of the church, the Creeds, etc., are all saying the same thing that the apostles said.
Protestants typically speak of the Bible as authority because it is a special revelation (Catholics would agree with this but it isn’t their main point). Both place the Bible in authority but for different reasons, and the Catholic reasons are such that the Bible stands alongside other teachings. There is no need to put the Bible and the Pope (or any teaching tradition) in opposition to one another because (according to Catholics) they are saying the same things. Many Protestants think that the authority given to the Pope (and the bishops) makes them a higher or equal authority to Scripture. Rather their interpretation of the Bible, which is their authoritative book, is considered the official or authoritative interpretation.
If interested, read the preface to the Assemblies of God’s doctrinal statement and you will hear them regard their interpretation to be an official/recognized interpretation of Scripture. I don’t think such a distinction is problematic, unless you happen to disagree with contents. Those that disagree with the contents are likely to say that the other group is placing that teaching equal with Scripture (just as many Protestants accuse the Catholics of doing).
I think the celibate male priesthood alone is enough to prevent Protestants from becoming Catholic. I have written extensively what I think about women’s ministry, so enough said on that. As had been pointed out to me, their are a number of social teachings (abortion, birth control, etc.) which are also not likely reconcilable between Protestant and Catholics. These differences are likely not reconcilable. I don’t think any would deny that. But I think Protestants would do well to consider whether a disagreement about birth control, papal authority, and the like are good reasons to regard Catholicism as something other than Christian.
The differences named here closely parallel reasons that many Protestants give as markers of Catholic unfaithfulness to what they consider to be basic Christian truth. I hope I have explained these such that the actual Catholic ideas are illuminated as similar to but different than what all Christians believe. These reasons may be good reasons for Protestants not to become Catholic, but not good ones to defame our Catholic brothers and sisters. Put another way, these are good reasons that we cannot reunite. However, our differences are not ones which prevent us from meaningful fellowship.
If you really want to understand Catholicism, I recommend the works of Robert Barron. Barron is a theologian and priest that has a knack for making Catholicism clear.