Paul had the council of Jerusalem in Acts 15 verify that the Judaizers weren’t even preaching the gospel in the first place.
So, the gospel is not “circumcision + Jesus”.
The gospel “whoever believes in HIM shall not perish...”
And then God is able to finish the work which He began in you. “being confident of this, that he who began a good work in you will carry it on to completion until the day of Christ Jesus.” Php 1:6
Sure, John 3:16 tells us all the believing ones will not perish and have everlasting life, but that is not the whole gospel, not even close. It says nothing of sin, nothing of repentance, nothing of the resurrection, nothing of imputation, nothing of Christ as a substitute for sinners, etc. That kind of mere Christianity approach will send people straight to Hell. We can say we believe in Jesus and believe all sorts of wrong things about who He was, why He came, and what He accomplished. And when we do that, we believe another Jesus and another gospel.
It’s dangerous to try to say any one verse is the gospel, but if I had to pick just one it would be this:
“For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.”
—2 Corinthians 5:21
But some men came down from Judea and were teaching the brothers, “Unless you are circumcised according to the custom of Moses, you cannot be saved.” - Acts 15:1
You mentioned Acts 15 and said they weren’t teaching the gospel In the first place. I agree because they were adding to it, rendering it a false gospel. And it’s clear from verse 1 they were attempting to add circumcision, just as I stated earlier. They were adding to the gospel of grace, just like Salt Lake City does and just like Rome does. The Bible is clear, grace and works cannot mix. It’s either by grace alone as the Bible says or it’s of works. It can’t be both. Any religion that adds law-keeping for salvation isn’t biblical Christianity.
“And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then is it no more grace: otherwise work is no more work.” Romans 11:6
8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: 9 Not of works, lest any man should boast. 10 For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them.
—Ephesians 2:8-10