Moral training serves the society that institutes it by rendering the individual amenable to control by others when that would benefit the society and averse to control by others when that would work to the society's detriment.
Now here's a little test: If you agree with that assessment but think it describes a dark side of the social contract, you might be a progressive. If you agree but think it describes an essential and benign feature of the social contract, you might be a conservative.
That's not all there is to moral training but in respect of what orders and suggestions we will take and which we will ignore, that's pretty much the program.
Culturally homogeneous societies pull this off...even at a cost to personal freedom of conscience and expression that is seen as oppression elsewhere. Cultural pluralism requires tolerance of a containing, simplified super-culture. When that tolerance is dispensed with, when one of the societies within the larger society holds that its views cannot be contradicted by the actions of any element of the larger society, fragmentation ensues. The essence of the contract of pluralistic societies is tolerance, a agreement that you will just put up with people who don't share all your beliefs as long as they don't hurt you and leave you alone to put your values into practice within your own group. The arrogance to abrogate that tacit treaty of tolerance is expensive: no appeal to common sense or fairness is left with any force should a group find its beliefs under censure following an attempt to impress its moral training on the broader society.
It is arrogance, it is not a right.