Agreed to some extent, however, I subscribe to the idea in Proverbs "Train up a child in the way he should go: and when he is old, he will not depart from it."
If you have beliefs about life and the world which you think are important to survive and thrive, I think it is your duty to pass that on to your kids as best you can.
Of course, your kids are autonomous beings, and have to make their own decisions ultimately. You expect them to reject the classical teachings and make all the typical mistakes when they are growing up and finding themselves as individuals. As you say, you shouldn't reject your kids as part of that process. Rather, like the prodigal son you have to have faith they will make it back to the right path once they've worked out what the wrong paths are.
I would say that goes for classical wisdom concerning right vs wrong as much as that also goes for hard money, the evils of debt, the importance of savings, etc.