I think that there are three issues that are critical to the fabric of the various churches.
OK, let's look at these issues.
REAL PRESENCE
i've looked at a few things about communion by Baptists. The problem is that their statements are primarily negative. However as far as I can tell, they see it as a memorial, in which we remember and give thanks for Christ's death for us. The bread and wine are symbolic of Christ's body and blood. So how close is this to the other end, which is Lutheran and Calvinist? I think substantially it is fairly close.
There's an unreasonable tendency among "high church" Protestants to disparage the terms symbol and remembrance. But a symbol is a visible sign of something beyond it. That's exactly what almost all Protestants think the elements are. Similarly in remembrance, if done seriously, I think someone would be spiritually communing with Christ's body and blood.
Similarly I think there's an unreasonable tendency among Baptists to misinterpret other Protestants' language. Thus they reject the sacraments as sacraments, even though treatments I've read agree that they are signs that point to things Christ has done, which is consistent with the usual definition of a sacrament as a visible sign of a spiritual reality. The rejection of them as means of grace seems to me to be based on the Catholic concept of grace as a fluid dispensed by the Church, and not as the usual Protestant definition of grace as a disposition of God to save us.
It is clearly the case that Lutherans, on the one end, and Baptists, on the other do not have the same description of the Lord's supper. I don't claim that Protestants agree on everything. However I think our focus on verbal formulas unnecessarily divides us. The Lutheran confessions do say that we take Christ's body and blood orally, which surely Baptists and even Calvinsts do not accept. Yet despite this, the Solid Declaration in 104 and105 makes it clear that while the mouth participates, the mode in which Christ is present is spiritual, so that "through faith true believers are in the Spirit incorporated into Christ, the Lord, and become true spiritual members of His body." Surely Baptists and Reformed would agree with this. Despite the confessional documents' vehement rejection of Calvinist spiritual presence, I believe that Calvin's concept of spiritual communion with a body that is physically in heaven, and the Lutheran concept of a body that is actually present with us, but in a spiritual rather than a physical mode, is substantially the same thing. And that the Baptist concept of the elements as signs through which we remember Christ's acts for us in faith is likely to be in practice what I would refer to a spiritually communing with Christ's body and blood.
DOUBLE PREDESTINATION AND FREE WILL
Why do the PCUSA and ELCA see ourselves as cousins on this issue? Because we both believe that we are unable to do anything for our own salvation without God calling us. In fact the Lutherans and Reformed agree on how justification happens. Where we disagree is whether it requires cooperation for us to continue in that state. And even there, I think this is a matter of viewpoint. Calvinists maintain that our justification, from the beginning to the end, is entirely God's work. Yet, we also admit that people do fall away. We say that in reality, they weren't saved to begin with. But that's God's perspective, which we certainly don't have. From our own perspective, people certainly do fall away. But Luther is fairly clear that he does not believe we can see things from God's perspective, and that it is a mistake to try. So I believe Lutherans are explicitly referring to how things are visibly, while Calvinists are giving a description that only makes sense from God's perspective. I must say that as a Calvinist, I have a lot of sympathy for Luther on this point.
Most generally, I think there are two concepts of the relationship between grace and free will, which do in fact differ, but in a way that should not break communion. We all reject the extremes: that we are able to respond to God's demands on our own, and on the other end that God forces us to do things and so we are not responsible. Everyone agrees that salvation is based on God's gracious actions, and that we make real choices for which we are responsible. So we both think that God's grace and our will are essential. The question is how we see the relationship between the two. Calvinists almost always believe in compatibilism. This sees God as wholly in charge, but it also sees that there are two levels of explanation. If you look at things from God's perspective, everything happens in accordance with his plan. Yet, they happen through secondary causes. We make real decisions for which we are properly held responsible, even though they are part of his plan. Arminians have the same two considerations: God's actions and our responsible decisions, but rather than the two levels of explanation of the compatibilist, they see them as interacting in such a way that they can't be separated. In both cases we maintain that God's will and our responsible choice are both essential to a full account, but Arminians say that they interat in such a way that both are responsible, and Calvinists say that both are responsible, but on different levels of explanation. I think these are both attempts at talking about the same thing.
VISIBLE CHURCH
This is another area in which I think there's unnecessary conflict. Many Protestants have chosen to deny the existence of a visible Church. What they mean by this is that our true union is in Christ, and it is not represented by any one ecclesiastical body. Personally I prefer to say that there is one Church, which is visible, but that this visible Church is present in a number of different ecclesiastical bodies. At any rate, I believe this point is different from the other two, because it is really a Protestant-Catholic argument and not an intra-Protestant argument. And I think that even in the Protestant-Catholic argument, there's a fair amount of ideological manipulation of definitions to emphasize disagreement.
But I do think there's more substantial differences between Protestant and Catholic theology than within the Protestant tradition(s), and that some of those differences matter.
