The poem found in 3.4-7 lays out for us the foundational Christian truth that really, God has done and provided everything so that we can have everything. Today, Paul reinforces this and encourages Titus to platform his teaching on this, and for good reason…
The saying is trustworthy, and I want you to insist on these things, so that those who have believed in God may be careful to devote themselves to good works. These things are excellent and profitable for people. But avoid foolish controversies, genealogies, dissensions, and quarrels about the law, for they are unprofitable and worthless.
These things seems to refer back to the truths found in vv.4-7, simply that God has provided everything we need for salvation. Paul insists that his young charge platform his teaching on this so that those who have believed in God may be careful to devote themselves to good works. This is not Paul going against salvation by faith alone, rather, saying look, now that you are saved by faith alone (so that those who have believed in God), this is how you show it (may be careful to devote themselves to good works).
This needs to be the focus of our teaching in churches and this needs to be the foundation for our individual Christian lives: our conduct demonstrates what we believe and have received. I read recently that faith alone saves, but faith that saves is never alone! Our theology is grace-based, our ethic is gratitude-in-action.
Paul goes on to say that we are to stay away from secondary and non-essential issues in the main teaching time of the church (remember the context, Paul is writing to Titus as the Pastor of this new church). Foolish controversies, genealogies, dissensions, and quarrels about the law can, in some contexts and settings, prove very interesting, thought provoking, and useful, but as the steady diet of the assembled church, a Christ-centered, God-honoring, Spirit-empowered teaching time is a must.
Really simply for you and for me, Titus 3.8-9 teaches us that the main thing must remain the main thing. Titus was left in Crete to put things in order and to build up the saints for the work of ministry (1.5 cf. Ephesians 4.10-12) and teaching sound doctrine, based on the truths of 3.4-7 is a great start.