There are two major perversions of the gospel that have existed since the time of the New Testament. Both are derived from merely adding Christ to one’s life without giving up what was driving one’s life to begin with. The one from Jude 4 is the antinomian version (loose-living) as is refuted in books like James and 1st John. This perversion states that there are no moral standards of holy living, basically promoting a view that Christ offers forgiveness of sins for all, but that salvation may or may not result in power over sin.
The other is the legalistic version as is found in Galatians, which requires an addition to Christ’s work in order to be justified. In giving those descriptions, you can see how the Gentiles would be tempted to just add Christ to their pagan lifestyle and the Jews would be tempted to add Christ to their legalistic lifestyle. Both have to be instructed in the NT to completely turn away from their former life so that Christ may be honored. In Acts 15, we are dealing with the Jewish perversion of the gospel, since they are explicitly teaching that circumcision is required to obtain a righteous standing before God.
Again, the threat to the gospel in Acts 15 is adding something to Christ’s work as a requirement to be saved. It was Christ plus circumcision leads to justification. In our day, there are examples of false teaching that promote Christ plus the eucharist or Christ plus baptism or Christ plus sabbath keeping that leads to justification. And of course any requirements needed in addition to Christ’s finished work to be justified, implies a subtraction from the absolute sufficiency of Christ’s work.