Although every one comes on the earth on a clean slate and pure from all sins, but sometimes the parents do have a role in the future of their children specially if they have sinful lives and haven't repented and not tried to warn their children about the punishment of evildoings.
If parents have sinned but asked for repentance, then the children will have a better chance of being inclined towards the truth and be faithful. In both cases, the child when comes of age has a free will to choose between good and bad and although it becomes difficult to be on the right path for the children whose parents are sinful, it still isn't impossible.
Those whose parents have repented after sinning or are among the faithful ones are more inclined to be on the right path although they can always be misguided because of shaitan being our open enemy and the vicious self which moves us towards evil.
Children will face the consequences of their misguided parents but will not be accounted for their parent's sins.
A verse in the Holy Quran points out to this indirectly also stating the fact that not only is it the duty of parents to warn their children but also if they don't do so, then they will cause their children to also end up in the hell fire with a painful punishment.
The verse is in Sura Tahrim ayat 6 which says,
O you who have believe, protect yourselves and your families from a Fire whose fuel is people and stones, over which are [appointed] angels, harsh and severe; they do not disobey Allah in what He commands them but do what they are commanded.