If parents now choose to press bigotry or other anti-social ideas on their children, their children are, at least, exposed to competing ideologies in a relatively free and increasingly prevasive marketplace of ideas. You understand, then, that any Federally mandated and funded educational cirriculum is unlikely to give ascendency to the ideas you champion. Your system would, in essence, ensure that children are not exposed to the very things you believe they need to learn. A curious solution. See 1 above.
Parents can make inappropriate choices.
So can governments. Measures begin with exploring the reasons the child in question is visiting the site at issue. Maybe he or she has questions about racism, sex, etc. I have not, as of yet, had to take anyone out behind the garage and shoot them. But it can also choose not to.