InformedIgnorance
Do you 'know' or believe?
I do not have children (though I have Godchildren despite their parents being aware that I do not share their Christian faith - go figure) however were I to have children I would not be concerned with regulating their choice in beliefs, just as I would not be concerned with regulating their choice in sports (I would however encourage them to be active and to be mindful of others, thus to exercise good sportsmanship).
Instead I believe that it is the parent's role to encourage their children to obtain (and to actually use) different tools - ways of thinking, of examining their environment, what they are being told and so forth as well as a general framework by which to guide their life, i.e. to provide a vague system of values. It is these different tools and guidelines that parents are supposed to provide, not some arbitrary belief system.
Instead I believe that it is the parent's role to encourage their children to obtain (and to actually use) different tools - ways of thinking, of examining their environment, what they are being told and so forth as well as a general framework by which to guide their life, i.e. to provide a vague system of values. It is these different tools and guidelines that parents are supposed to provide, not some arbitrary belief system.