If the one is forced ideology then the other is equally forced ideology.
You know, by telling them " how they can and can't express themselves", as you stated above.
So we all agree that both are forced ideology.
That leaves whose forced ideology should be employed.
If it's your kid, then whichever ideology you want to force upon them is the ideology employed in your household.
Those outside your household that find your ideology unacceptable can demand their children not be exposed to your doctrine by you, schools, or interaction with your child.
You wouldn't force a Catholic catechism class on Muslim kids or vice versa would you?