The Scottish Presbyterians on How to Think of a Schismatic Church

James Walker, in his highly regarded work The Theology and Theologians of Scotland (Edinburgh: T. and T. Clark, 1872), discusses the doctrine of the visible church held by the Scottish Presbyterian theologians during the period when the Westminster Standards were written.  In this quotation (pp. 103-104), he points out that the Presbyterian theologians of those days understood the historic concept of schism--that it is something different from heresy and involves even otherwise orthodox churches or Christians who separate without cause from the rest of the catholic visible church.  Walker also articulates a de facto / de jure distinction as a part of the Scottish theology of the period.  A schismatic church might still be considered a church in terms of being, while yet, because it is schismatic, it does not constitute a church formally or de jure.  This is very similar to Calvin's comments regarding the church of Rome in his Institutes.  Here's Walker:

In regard to the former point, the point in hand, it seems to me quite clear that a very high doctrine of the Catholic visible Church was the doctrine of these old days.  Schism was a great reality.  The question was not merely whether a certain community of professing Christians was orthodox and pure, but whether it belonged to Christ's visible empire.  The Donatists held the fundamentals, yet they were to be abandoned for the Catholic Church.  It is not clear to me what, according to this view, was the exact position of a schismatical Church.  If it had the main truths, it was still a Church,--a Church, I think they would have said, in concreto and materially, and salvation work might go on there; but formally and in abstracto, it could not be recognized as a Church, or communion held with it as such.  A Church regarded as schismatic could only hold its ground on the principle that severance was necessary, because communion was no longer possible or lawful on Catholic communion ground. . . . The doctrine I have briefly explained was the doctrine eminently of the Confession period,--the doctrine of our Presbyterianism in the day of its power and its glory.

For more, see here and here.