Divisive, ungodly "dreamers" had entered the church and advocated for a change of direction. But their changes appear to be based more on behavior (blasphemy, division, and disruption) than on teaching. Of course, teaching would be at the core, but Jude wants his readers to be on guard against this divisive disruption.
How should the church today continue to "contend for the faith"? Certainly, we need to guard our doctrine. But we also need to guard our own motives. Jude says that these dividers "rely on their dreams" (8). Evidently, their own experiences and ideas caused them to become divisive and seek their own way. We do the very same thing today when we allow our opinions to become divisive.
Jude provides a simple solution to ungodliness and division--seek your own spiritual growth and that of others (20-23). Divisive people are devoid of the Spirit (19), but godly people build themselves up in the faith and pray in the Spirit. They mercifully watch out for others and work to build up their faith. They never lose sight of Jesus' impending return, and they keep spiritual growth--theirs and others'--front and center.
That is what it means to contend for the faith.