Earlier quoted context omitted.
For an extreme example, suppose stormfront camps outside your child's school passing out leaflets and having fun, racist singalongs. How can it be your responsibility when they're in an area that is effectively outside your control? Sure, once you find out about it you can pull them from school but this requires first that you find out about it, which you may not be able to do until they come home singing the 14 word…
Why are you worried that your children will be threatened for their heritage in a world where children can be exposed to a diversity of opinion, including those you don't approve of? Do you think you'll lose the war of ideas to "bullshit"?
After all, nazi did won war of ideas and so did hutu and so did khmer rouge.