As I said, I think if you ensure economic equality for everyone, the problem will solve itself soon enough.
Having said that, if you want to tackle the problem of discrimination separately (e.g. because you believe you can solve more quickly and easily than the economic inequality problem), then the tactics currently used (i.e. feminism - complaining, protesting, self-victimisation, and shaming reasonable conter-arguments) are the wrong way to go about it.
Lets for a moment consider a similar, yet different problem. Rape. Men are statistically more likely to rape women than women are (feminists are happy to point that out). I don't think it's correct to villify men as a group for that, but I do think it's reasonable for women to be extra cautious when interacting with men (e.g. it may be a better idea if a drunk woman asks a female friend to take her home, than a male friend, or to cross the street to avoid strange men at night). Nothing personal, just statistics - and oponents can scream "sexism" as loud as they want, but you can't put a price on personal safety (of course, feminists won't scream "sexism" in this istance, because it's fashionable to shame men).
Same with blacks and crime. Blacks statistically commit more crime, so it's not unreasonable to be more afraid of or cautious with blacks than with whites (or asians). Sure, it could be plain racism (pre-judice), but it could also simply be pattern-matching based on statistics (post-judice). And even if you consider those instincts to be wrong, it's hard to fight against them, after all they've been keeping us alive for thousands of years!
If you nevertheless want to fight those instincts, I guess the best way is more information, and emphasizing that people should be treated as individuals, not as a group. Unfortunately, feminism/social justice/identity politics isn't very good at either. In particular, if you attack (verbally or physically), shame, fire, riot against those whose opinion you want to change, I can't imagine you'll achieve much.
Anyhow, that's my thinking, although I fully accept it's wrong/there's more to it - here in the EU, I'm quite a bit removed from racial issues...