The answer to racism isn't really not-racism. The key function of racism is to be able to differentiate between what defines a good person and what defines a bad person. In that, racism is found wanting, because it doesn't have guidelines.
The human mind, from Adam, who was taught the names of creation, was designed to differentiate, to tell the difference. To discern, to evaluate, to assess, to test, to define. But racism is taking someone else's definition and without evaluating, using it to blanket everyone who share similar attributes.
Thus, we want to teach our children the science and art of evaluation of the human being. To know what are qualities of a good person, irrespective of race, religion, age, gender or preference. There is a level of humanness that transcends all of these that we need to be able to recognise.
Since humans tend to cluster socially around similar beliefs and the strength of those beliefs, the next step would be to evaluate whether these other people share your beliefs and whether you would want to interact with them.
Islam has moral guidelines and measures that help with this decision, but also warns against taking them as absolutes, and reminds us that we don't really know people.
Thus far, the last four paragraphs sounds a lot like racism, but this is where Islam (and as pure messages of the Divine, should other revelations as well), trumps racism by going one step further: Da'wah.
Da'wah is essentially wanting what is good for yourself to be good for your brother. You promote Islam to others, because of the peace and empowerment it allows others, not because you think they're stupid without it.
And since da'wah is meant to be for all, and if you are a true da'i you really don't choose to avoid or ignore anyone, simply because, irrespective of how they behave, you believe they deserve to be good.
So, the answer to racism isn't non-racism. It's learning to evaluate and then learning to help.
(For Muslims, the short answer, is Islam).