1 Timothy: 4 nor to pay attention to myths and endless genealogies, which give rise to mere speculation rather than furthering the administration of God which is by faith
Paul wasn't telling Timothy or other Christians to not do geneology.
Timothy was in Ephesus setting up the Church there, particularly choosing Elders and leaders for the Church. Paul was telling Timothy to pick those that taught sound doctrine, not those that proved they were the most qualified by giving a geneology down to whoever, and not those that told myths about themselves as to why they should be the leaders.
Similarly in the modern LDS church we are also not supposed to pick or call leaders based on their geneology, but through prayer and the spirit, whether they are converts or generational members. Yes I'm talking about Stake Presidents and Bishops that seem to think that converts aren't good enough to serve in church leadership callings.
It also serves as a warning about those that profess that since they are descendant from some leader they somehow have better doctrine then the Church itself does. Yes I'm talking about Sandra Tanner.
Sounds to me like Paul was warning the folks in Ephesus not to get sidetracked by myths and false teachers (like the Mormons)
Warning Against False Teachers of the Law
3 As I urged you when I went into Macedonia, stay there in Ephesus so that you may command certain men not to teach false doctrines any longer 4 nor to devote themselves to myths and endless genealogies. These promote controversies rather than God’s work–which is by faith. 5 The goal of this command is love, which comes from a pure heart and a good conscience and a sincere faith. 6 Some have wandered away from these and turned to meaningless talk. 7 They want to be teachers of the law, but they do not know what they are talking about or what they so confidently affirm.