Would the guy have to remain celibate?
1. If he had sex with probably tens or hundreds of thousands of women over the millennia he would have god knows how many grand children all over the world depending on how many "greats" there were, that means any woman he sleeps with could be one of his grand children meaning INCEST.
2. Its legal to have sex with or marry a cousin as long as she is not the first or 2nd cousin (3rd in some parts of the world). It is actually fairly common for people to find out they are married to tenth cousins (happened to the actor Kevin Bacon). But that is different from being someone's parent or grand parent.
3. Laws do not really exist for this since nobody lives long enough but if human life spans for some reason were to commonly become hyper long would laws have to be passed similar to "cousin numbers" where at some point if there are enough "greats" it becomes legal to have sex with a grand child? Such a law would need to exist for the character in this movie because keeping track would be too difficult and the only way to guarantee he is not guilty of some form of incest would be to be celibate forever.