Abraham Kuyper proposed a doctrine known as sphere sovereignty. I'm simplifying radically, but his view was that God operates through three basic spheres, that of the family, the church, and the state. The family is the most basic of the three and predates the others, and at some times in earlier history (Abraham and Moses, for example) the covenant heads in the spheres were identical.
However, under the current conditions, the government of the family, the church, and the state are and ought to be separate. That means while the confessions of the church quite properly prevent Roman Catholics and conservative Protestants from being in the same churches, that doesn't mean we can't work together to stop abortion, for instance, under the principles of Romans 13 in which the primary purpose of the state is to punish unbelievers.
If I were in an overwhelmingly Roman Catholic country (Cold War-era Poland, Franco's Spain, etc.) where patriotism and Roman Catholicism were closely linked, I would have significant problems cooperating with Roman Catholics. Roman Catholics in the Deep South had that problem a century ago as well dealing with the Bible Belt, when anti-Catholic efforts were made (wrongly) through Blaine Amendments to drive Catholicism out of the public schools which were at that point still largely Christian.
We're not in that situation today in America and we need to “hang together” whenever we can or we will most certainly be hung separately by the radical secularists.
We most certainly do. When I was in school a professor once took a large sheet of paper and drew a dot on it and then asked each of us to describe what we saw. Invariably we all concentrated on the dot which accounted for something less than one tenth of one percent of the total area of the paper. No one really commented on the other 99.9%. We tend to do the same thing in these forums. We have significantly more in common than we hold differently. When we both profess that Jesus is Lord and Savior we have stated the 99.9%.
Eccumenicalism and cooperation is an area we have to trust to faith. Agreeing that it is not a recruiting tool or a negotiation, we must rejoice in what we have in common and respect what we as individuals hold different and work for the Glory of God, not ourselves or our denominations.
I have to say that as a Catholic I am prepared, in order to confront the threats to Christianity and to religious freedom, and to protect life and traditional marriage, and our liberties, to embrace what I do not yet know and accept what I do not understand, and trust that God will guide our efforts. I have faith that the separated brethren will stand with us. Peace be with you