the bible warns us many false teachers will arise to deceive the believers (2 Peter 2).
We are taught to discern (1 Thessalonians 5:21).
There are many disagreements among Christians on unimportant issues, why can't people just stick to Jesus's core teaching? Yes, many things are unclear to us, but if we all start to speculate, there's how the church got split.
Don't get me wrong, I'm not a liberal Christian who accepts things like LGBT, but sticking to the main message of Jesus and the apostles doesn't seem hard.
I don't see what the Bible texts you reference, have to do with defining what the core teachings of Christianity are.
Anyone, who believes anything, can reference these Bible texts.
Some groups appeal to sticking to the "gospel".
They may assume that this label, points to a universally agreed on body of doctrine.
But it does not.
Sticking to the early creeds of the united Church, at least has historical support.
But many Protestant Fundamentalists reject this historical definition of core Christian doctrine.
Some groups appeal to the New Testament teaching. But most of them cannot agree on
who authoritatively interprets the Scriptures.
Some groups appeal to the "guidance of the Holy Spirit". But this does not include
a builtin "decision algorithm" to determine who is being guided by the Holy Spirit.
The united Church, for the first 1,000 years, appealed to the authority of the 11 Apostles
(and Paul) to determine what the canon of Scripture was, and what authoritative
teaching was. This is based on the great commission, to the 11 Apostles.
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Asserting that Christians should stick to "core teachings" is useless rhetoric, without
a historic definition of how this core teaching is to be authoritatively determined.
I point this out, because many modern Christian groups have NEVER thought
seriously about how the "gospel" or core teaching, is to be authoritatively defined.
But, the ancient unified Church, has.