Unless – though I know of no such societies in the real world – one lived in a world without the tensions and evils of racial prejudice and racism, I don’t think it’s possible to be a contemplative Christian and not be openly anti-racist.
So, what’s a contemplative to do? I’ve mentioned a lot of things in the past. The position of the contemplative soul in the face of “social issues” cannot be indifference. That would be failure. Why? Simply because social issues involve power (racism involves the use of varieties of power against real human beings). And power involves human relationships. Human relationships demand love. And love, which is the will of God, is at the heart of the contemplative path.
In these kinds of things, it’s not enough to “not be racist”; what’s important is to do things and “be” someone who is opposed to racism. One has to be “anti-racist”; it’s too poor to be “not racist”. This is like the spiritual life, where the saints say that, if we’re not moving forward, we’re moving backward. Social issues, like racial prejudice and racism, are like that, too. If we’re not fighting them and if we don’t have progress in ourselves about overcoming them and standing against them, then we’re falling backwards.
How can one go forwards, not backwards? How can we become anti-racist? If I could give just one recommendation regarding racism, I’d suggest you check out A Beginner’s Guide to Anti-racism for White People, by a fellow white person (in fact, by one of my friends). It’s written from the perspective in America, but the truths this Guide touches on have a much wider application.
Contemplative in the Mud 
Yes. I believe we are called to remove any and all barriers between ourselves and others. Like you say, this has to be active, not just passive. Jesus was never passive. We are His hands and feet. We are the Body.