One of my readers has remarked, "Every denomination seems to have it's own set of core doctrines," and asked "How would you define the core Gospel?"
I replied with a question of my own, "What do you mean by 'core' Gospel?"
And the reason is this: The Bible doesn't seem to encourage us to think in terms of what is 'core' vs what is 'peripheral' (Unless we're in the context of a Romans 14 discussion). Instead we're asked to think about that is 'true' Gospel or not; what is 'same' vs what is 'different'. E.g. Galatians 1:6-9. It's either in or out of the Gospel; on or off track; part of or not a part of and so against.
Of course the Gospel message is as big as Genesis to Revelation, but can be summarised as simply as "Jesus is King".
Paul's rebuke in Galatians 2:15-21 picks up the centrality of God's grace in justification by faith through the death of Christ. But it would be a mistake to look at key passages like these and relegate other doctrines, for example our doctrine of creation, to the 'non-core' bin. In 1 Timothy 4:1-6 we see that our doctrine of creation is pivotal to pure doctrine generally.
Every doctrine of the Bible is interrelated and interdependent. And so we're on dangerous ground as soon as we start taking any aspect of the Bible's teaching and putting bits into the 'essential' bucket and others into the 'optional' bucket. For example, if we say that the doctrine of creation is core but the Sovereignty of God not; or repentance is core but baptism is not.
If the Bible teaches it, it is core. All of the Bible's message is the Gospel and it is all essential.
Yes every denomination has differences and commonality in its beliefs compared to others. And if any of these teachings, as with any of our own beliefs, are contrary to the teaching of the Bible at any point, then we/they are in error at that point need to repent for being against God's word.
When I get to it I do hope to clarify what I believe the Bible's essential gospel message is: what I've phrased elsewhere, "the gospel of the Apostles of the New Testament" -- the message that was entrusted to the 12 apostles and to Paul, who even refers to it as 'my gospel'. Anything else was'another' and 'different' gospel and so false (See Romans 1:1-5; 16:25-26; cf. Rom 2:16; 2 Timothy 2:8).
Romans 1:1-5:11 is a brief unpacking but the whole book of Romans is a fuller explanation of the Apostle's gospel. Galatians starts with is a defense of Paul's apostolic authority and sets a good context for beginning to understand the uniqueness of the Apostles authority over the message and our dependence on them (Galatians 1:1-12ff.)
And hence the authenticity of the gospel is also strongly dependent on their Apostle's authorship of the New Testament, and so it's consequent authority. We need to go by it rather than denominational formulations or systems of doctrine constructed to sit over the New Testament.