Our family goes back to William the Conqueror as well.........
After Cromwell's death and the restoration of the Stuart monarchy, transportation to the colonies became a popular way to deal with petty criminals and paupers for whom there was just no future in Great Britain. Accordingly, the lines back to royalty become less common at that point.
But a clear majority of the pre-1650 puritans and their off-shoots such as the Anabaptists are only a century or so removed from the Plantagenet royalty which descends from William. My personal theory is that the Plantagenets turned to religion after they lost their position to the Tudors following the battle death of the last Plantagenent King Richard by the forces of Henry Tudor at the Battle of Bosworth Field.
If you are interested in trading family research notes, feel free to freepmail me with any details you might have and I may be able to help you fill in some gaps.