That's an interesting point. I have noticed that often ideologically motivated parents don't always produce the same ideologically motivated offspring. They'll have to have very strict rules and some kind of brutal indoctrination to ensure the next generation follows the same path. But the more brutal and severe it is, the more likely it will cause rebellions.
I can already see a tragi-comedic scenario: the new generation overthrows the old guard, slams on the brakes, ship takes years to slow down from almost light speed. Decades later they are finally going back to earth at full speed. Now the next generation looks back at the mess their parents made, rebel, overthrow the old guard, slam on the brakes, decades later they are back flying to the original destination. But not until the next generation decides to bring back the fire of the revolution and turn things around... It all ends with them running out of fuel.
The pessimistic view is that we'll just have to let ChatGPT drive the ship and knock everyone out in cryosleep so they don't mess with the ship.