The genealogies leading to the Messiah, Jesus Christ, are vitally important as supportive proofs of his being qualified as God’s Messiah (Matthew 1:1-16; Luke 3:23-38). So we definitely do need them, and should pay attention to them. Other Biblical genealogies, while being important for historical purposes, so we should be aware of them, but, nevertheless, are not of great importance for Christians. Please see the other two articles on this site about genealogies.
Beyond what is mentioned above, Christians are warned:
“Stop teaching false doctrine and occupying themselves with myths and endless genealogies. These myths and genealogies raise a lot of questions rather than focusing on God’s plan, which centers in faith” (1 Timothy 1:3,4 GWT).
“Avoid foolish controversies and genealogies and arguments and quarrels about the law, because these are unprofitable and useless” (Titus 3:9 NIV)
Apparently some first century Christians were indulging in unscriptural “controversial speculations” (NIV) that included “endless genealogies” (NIV), and “arguments and quarrels”. So Christians today can take this as a warning against doing the same things. This doesn’t mean that we shouldn’t study study, discuss and examine different interpretations of the scriptures. The warning is actually against “genealogies”, petty quarrels and “speculations” that “go beyond what is written in Scripture” (1 Corinthians 4:6 GWT). We should engage in honest discussions of the Bible that lead to wisdom (Acts 17:11; Proverbs 17:17).