No, no, no. This is ridiculous, and worse, dangerous to the agenda of anti-racism. The idea that ‘race is a fairy-tale’ is so obviously false that you are losing credibility on all fronts. It’s true that there’s no such thing as a ‘pure’ race (most everyone has a bit of lots of different stuff), but does anyone doubt that Chinese people tend to have black hair, and Germans not so much?
Second, I disagree with your notion of what ‘racism’ is — racism is a belief that people of certain ancestries should be denied the rights given to others of ‘good’ ancestry. All of the racist outrages still committed daily in this country stem from this notion — stop-and-frisk, differences in drug sentencing, etc. are all about differences in the rights and privileges accorded to people of each race.
Trying to counter racist attacks with “race isn’t real” is dangerous because you are tying your effort to the defense of something false.