One danger of reducing “the system of doctrine” down to a generic “Calvinistic system” – such as we see argued for by Charles Hodge – is that such a move was not the original intention of either our American Presbyterian forefathers or the Westminster Divines. What is fundamental to our doctrinal standards? Is it Calvinism? I would hope so. During Hodge’s day there were considerable battles over soteriology, so we should not be surprised to see him reduce the system of doctrine down to Reformed soteriology.
“The words ‘system of doctrine,’ have a definite meaning, and serve to define and limit the extent to which the confession is adopted.” ~ Charles Hodge 
The Westminster Confession and Catechisms are a treasure. When people ask for a good one-volume systematic theology, I usually recommend the Confession and Catechisms. When I first became Presbyterian, I was under the assumption that we viewed the Westminster Standards as the system of Presbyterian doctrine because it is biblical. I do not mean that I viewed them on equal ground with Holy Scripture. I viewed them the way Thornwell did, “it certainly is a convenience to have the teachings of the Bible reduced to a short compass, and announced in propositions which are at once accepted without any further trouble of comparing texts.”
I came into the Presbyterian Church in America (PCA) after the passing of Good Faith Subscription (GFS). I have always heard that passing it was a hopeful attempt at resolving arguments in the PCA regarding subscription to our doctrinal Standards. If that was the original intent, it is worth asking ourselves the question “is it working?”
It was over 20 years ago that we decided on GFS, and yet at 2021’s General Assembly there was still a need to have a discussion – which was very well attended – between two prominent Teaching Elders on confessional subscription and unity in the PCA. I think part of our continued confusion has to do with how we understand the phrase “system of doctrine” in our BCO, “While our Constitution does not require the candidate’s affirmation of every statement and/or proposition of doctrine in our Confession of Faith and Catechisms, it is the right and responsibility of the Presbytery to determine if the candidate is out of accord with any of the fundamentals of these doctrinal standards and, as a consequence, may not be able in good faith sincerely to receive and adopt the Confession of Faith and Catechisms of this Church as containing the system of doctrine taught in the Holy Scriptures.” (BCO 21-4.e, emphasis mine).
I wonder if many who hold a stricter view of subscription have the same view as Morton Smith, who argued that “full subscription does not require the adoption of every word of the Confession and Catechisms, but positively believes that we are adopting every doctrine or teaching of the Confession and Catechisms.” I believe one could hold Smith’s view and still agree with BCO 21-4.e as it currently stands. The question is not over every proposition, but over every doctrine. Part of the confusion regarding how to interpret “the system of doctrine” and with subscription in general may be traced back to the published views of Charles Hodge.
Charles Hodge is rightly a giant in American Presbyterianism. However, he did contradict himself over the course of his writing on this topic of confessional subscription. Hodge at one place argued that “by system of doctrine, according to the lowest standard of interpretation, has been understood the Calvinistic system as distinguished from all others.” Hodge argued that the theology in question which is contained in the Confession is basic Calvinism. He wrote in his book on church polity, “It is one thing to adopt the system of doctrine contained in the Westminster Confession, and quite another thing to adopt every proposition contained in that confession. John Murray takes issue with Hodge’s statement here, “It needs to be pointed out that Dr. Hodge is not accurate…It is not simply the system of doctrine contained in The Confession that is adopted; the Confession is adopted as containing the system of doctrine taught in Scripture. John Murray gives an excellent short history of various General Assembly actions and statements on “the system of doctrine.”