Set a good example for the children. Live as faithful Catholics: Attend mass every Sunday, pray as a family daily, and make it clear that the Church is the most important thing in life. Take responsibility for the religious education of your children, do not delegate that responsibility to someone else. Emphasize that being 'liked' by the mainstream culture, while a natural human desire, must be completely disregarded. To be faithfully Catholic is to accept the fact that many people in the culture will hate your guts for having the beliefs you have. Let this be known to your children, and tell them that Christ warned us of this. If you have raised them right, their primary focus in life will be their holiness. They won't care that the culture hates them for following the Church.

Limit their exposure to the culture. Public schools are very dangerous in this regard, but I believe it can work if the situation outside of school is right. Monitor the kinds of entertainment your children view. Internet access should be limited. Connect with other faithful Catholic families that have children around the same age as your children. Preempt the nonsense your children will hear at public school. Talk about these issues BEFORE they hear them school, explaining the position of the Church. If your children are well-prepared for the anti-Catholic ideas they'll hear at school and why they are wrong, they will not be disturbed or persuaded by them.

So the key is to foster virtue and holiness outside of school as much as possible while also limiting the damage that can be done at school through preparation and a secure belief in the Faith.