Legal Question in Criminal Law in California

Yes. The state does not have the authority to deny anyone the right to have a family. Your question suggests, though, that the offender and the other parent (most sex offenders are men I will presume that this one is the father) do not live together. If that is the case and if both parents want custody, then the matter will have to be decided by a court. The court will surely take the father's background into account when making this decision. It will be one of many factors the judge will consider. How important that factor is in the decision will depend upon many things, including the specific crimes involved (some sex offenses are much more serious than others), how long ago they occurred and whether the father has kept out of trouble since then. It is possible that he will have enough positives going for him to win custody, especially if the mother also has serious blemishes on her record.