"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..." - Titus 3:9There is prohibition here but also positive instruction to stay true to sound doctrine and promote unity in the churches. No way Paul is telling Timothy and Titus to go for sound doctrine and to edit their scrolls to deliberately avoid parts of Scripture. Pursuit of sound doctrine comes from keeping Scriptural.
"...charge certain persons not to teach any different doctrine nor to devote themselves to myths and endless genealogies, which promote speculations rather than the stewardship from God that is by faith. The aim of our charge is love..." - 1 Tim 1:4
Pursuit of our own genealogies isn't something to get obsessed with, a Christian's genealogy in their new life is 'in Christ, son of the Father'. Ancestry doesn't define who someone is for good or bad. Obsession with who we're related to can certainly lead to divisions as we try and elevate ourselves or others, and the gospel stands opposed to that.
There are pitfalls in study of Biblical genealogy. Some of the lists tell us exactly why they're written as they are, some don't. Where they do that frames our study of them, it's not that there's necessarily a point to find in every name on the list. The point of studying genealogies is not for geeky knowledge gathering but to help us see the gospel more clearly, since the gospel is the subject of the Scriptures. Rightly studied genealogies help us to see clearly what is already in Scripture because they're a part of Scripture, they're no tool for wielding power but rather for advancing humility.
With those cautions in view I plan to turn to a few examples in the next few days.