The issue with this is who gets to decide who's bigoted/racist. You can stretch and twist those words pretty far. Some of the crazies on places like Tumblr are doing that as we speak. Surely you wouldn't want people like that to control the school system.
Anyone with common sense can see the difference.
And common sense is what needs to be taught at school and be promoted by parental guiding. The ability to think, to weight facts, alternatives and consequences against each other and the ability to independently decide for yourself instead of accepting others decisions when you feel they are wrong as well as the ability to reflect on decisions and if necessary reevaluate. And then, the ability to act on those conclusions, to change!
Common sense has to become common already. Reciting facts, doing math equations, etc. is great if we need drones to fill factories or bureaus, but what society needs to become something better is the ability to think critically and the ability to act on that instead of simply letting itself get washed away by the stream.
Right now, there's too many people that just do what they've been told to do without thinking for themselves. And in the everpresent social evolutionary process, the mass makes the man and individuals that confront the social norm, that want to change get opposed. Not because people decided that the result of that change is bad, but because the change itself is bad. When enough people developed the ability to reflect independently, the society as a whole can become malleable again. Likewise is the chance that such a society degenerates in some form of warped evil or whatever decreasing proportionally with the amount of people that can think critically.