There are many things we can do, here are some that I have been doing as a foreign student in the US and now an edcuator. And hopefully it would help sparking some more new thoughts.
Aim for promoting diversity, NOT eliminating racism
Politically, you will have a lot more buy-in in organizing a "diversity week" than an "anti-racism week." Racism is not something we can eradicate because it stems from the sense of superiority and difference in power, which will always exist in various degree. And in a personal level, given the same race/ethnicity, one person may think a certain treatment is totally fine while the other one may show a strong sign of being offended because the treatment promotes racism. You cannot win.
In most cases, the more one tries very hard not to be a "racist," the more difficult situations one can get into. A fun example: an African American colleague of mine went to watch 12 Years a Slave with her husband and after the movie ended, a white couple came up and said, sorrowfully, "You people really had it hard, didn't you?" I found that attitude of "We had treated your ancestors so badly that now I am going to make up for it," a bit of, well, racist.
Instead, promote diversity. Diversity is less "silo," it incorporates many other aspects like religions, sexual orientations, races, ethnicities, etc. What's more, it gives us some goal to achieve, something to build instead of some infinite amount of pests to destroy. This new goal will certainly improve your mental health and open up a lot more possibilities in improving the situation.
Promote critical thinking
Embrace critical thinking in both study and teaching. A lot of racism-related phenomena wouldn't pass the most fundamental critical evaluations. Equipping students with this invaluable skill will help them dissect the situation with higher clarity and certainty. Racism itself is very biasing, to the extent that it's nearly hilarious. For instance, if a member of Purple race commits an atrocious crime, the members of Green race tend to attribute the blame to the whole Purple race. While among the Purple race they tend to attribute the blame to the very criminal as a "bad seed," outlier, or isolated incidence. A simple thinking exercise on situations like this one opens up discussion among students quite well.
An additional benefit of being able to critically think on your feet is that you can instantly downgrade an intense racism argument to a logic-based, evidence-based discussion, pointing out the pitfall in their thought process rather than pointing out that they are a racist.
Know your history well, and be ready to listen to other's history
I found myself somehow have become the go-to person when someone has questions about my country. It is, to some degree, a polymorphic racism. Just because some girl is born in Japan doesn't mean she can dance like a geisha, just because some guy is from China doesn't mean he can recite all the characters in the Romance of the Three Kingdoms. However, I do take this consultant role seriously, and try my best to be an ambassador. I tell them the good, the bad, and the disgusting, no reservation.
Don't check your identity tags too soon
This is somewhat similar to that poor answer with like 10 down votes. Sorry to say that but I do agree with that answer to a certain extent. I have never sorted out a clear list of identities for myself. It's not like I am in denial, my identities are always somewhere but I don't tend to flaunt them right at the beginning of an interaction. I feel that in a lot of the times, conflicts happen because we decided that the action or treatment has clashed with our identity a little bit too soon: You said something against penguins, and I am a penguin, so I have to be upset now and punch you in the face. I would, instead, opt for understanding where they come from first. If the situation is non-hostile, I would proceed to explain (with critical thinking and evidence) that it's not always the case, and move on. You can correct the information, you can never correct a person's attitude, they have to do that bit by themselves.
Find an optimal environment
Lastly, it's important that you are promoting diversity in a place that you feel reasonably tolerable and accepting. This whole process of achieving understanding is going to be very long, and it's not worth risking your happiness or even life just because you want to make a statement in a hostile place. In conclusion, don't cave in, be present and remind others of our existence. They don't need to like us, but they do need to know we are here to stay, with a strong will.