It seems this topic is answers well enough.Pretty much. However, I wouldn't say "Protestants" since thats kind of broad. Anglicans have the branch theory, which accepts us and Rome as part of the Body....Evangelical Baptists most certainly do not
In summary, Protestants either say that Catholic Christians (ergo, Roman, Greek and Coptic alike) are heretics and apostates, or that "the Church" isn't an institution, but it's an abstraction known only to God.
Or, they might say that Catholics are the Church, but that they've been corrupted, the reasoning behind the Protestant Reformation in the first place, which is why the Protestants remain out of communion with it.
More or less.
Well, the topic is about "Protestants". Even though that is a broad brush, Unitarian Universalism on the one hand, and Trinitarian Calvinism on the other, that's what the OP is asking about.
You know, amusingly enough, the Puritan churches became a bit watered down, and started calling themselves Congregational, in the 18th century. And then starting in the 1770s, but really picking up steam in the 1780s after the Revolutionary War, there was a huge schism between Trinitarian Calvinists, and Unitarians, who took over Harvard Divinity School, the historic seminary of the Puritans. These early Unitarians were not universalists and many held to sola scriptura, but later in the 19th century the Universlist denomination began to thrive, and separately the Unitarians began to incline towards Universlism under the influence of ministers like Ralph Waldo Emerson. So the merger with the Universalists and subsequent complete apostasy of most of the UU church, starting in the 1950s and 60s, was inevitable.
Meanwhile the Trinitarian Calvinist segment of the former Puritan / Congregationalist churches wound up merging with the Reformed Prussian churches who broke away from the Lutheran Church - Missouri Synod, to form the United Church of Christ. As early as the 1940s, this denomination became increasingly liberal, and so many comgregations left to form the CCCC, the conservative Comgregational churches. I forget what each C stands for. In recent years the extreme liberalism of the UCc has caused them to shrink even faster than the Episcopalians, but there is a group of I think 75 conservative churches in the UCC that hope to one day restore aaa measure of orthodoxy to the denomination, called Faithful and Welcoming, and they run a sort of church Finder and social networking sites; I think there are well over a hundred UCC pastors associated with them, and they provide matchmaking services when a conservative congregation wants to hire a conservative pastor. This all works because, like the Baptists and the Unitarian Universalists, the UCC has a comgregational polity, allowing each church to chose it's own pastor.
But it's remarkable to note how the Puritans, the church of John, Cotton and Increase Mather, and Jonathan Edwards of "Sinners in the hands of an angry God" fame, the same church that burned witches at the stake in Salem, wound up through a schism dividing itself into what became the two most liberal denominations in America. And it's a bit sad to note that most of the oldest church buildings in America, including the oldest, are Unitarian Universalist churches, and those that aren't are mostly liberal UCC. One prominent exception is the Park Street Church in Boston, which I believe is CCCC. Also the Old North Church in Boston is Episcopalian and I believe due to its heritage extemely, shall we say, uncontroversial, recognizing it's status and value as a tourist attraction shouldn't be compromised by doing anything too shocking. But the oldest church building in America, the Old Ship Church, is tragically Unitarian.
Of course all these churches pretty much embrace an Invisible Church ecclesiology or a comgregational ecclesiology where the local church is the Church. But any anger they might have at Catholics is doubtless over the social stance of the Roman Catholic Church, the fact they have yet to yield on issues like the ordination of women or homosexuality. And in the Unitarian Universalist church this is probabaly fairly intense; the UUs pride themselves on inclusiveness and even have atheist ministers. So that's that.