If including your race gives you a leg up, then I think you should do it. I saw a whole lot of casual racism when I was in college, and if that was indicative of the experience of others then you don't owe the rest of us shit.
The ultimate goal from my perspective should be to eliminate implied tribal biases, rather than band-aid them. There's a fair bit of negatives with trying to force the issue with quotas, in my opinion -- by hiring on grounds other than merit, it might even perpetuate the bias. Those hired might for instance be thought of as "second class hires" within the company from the get go. So despite the casual racism that unfortunately exists, I can see why the poster leaves his or her race off applications.
In other fields, hiring can probably be done by ways that try to heavily reduce bias, and get similar increases in diversity without, from what I can see, the negatives of quotas. Some orchestras for instance have used "blind auditions" (https://en.wikipedia.org/wiki/Blind_audition) for quite some time, with a noticeable increase in diversity as a result. I see in the Wiki that some tech companies are experimenting with this approach. I'd strongly prefer this sort of system over what Google has (if the details described in the lawsuit end up being true).
In other fields, hiring can probably be done by ways that try to heavily reduce bias, and get similar increases in diversity without, from what I can see, the negatives of quotas. Some orchestras for instance have used "blind auditions" (https://en.wikipedia.org/wiki/Blind_audition) for quite some time, with a noticeable increase in diversity as a result. I see in the Wiki that some tech companies are experimenting with this approach. I'd strongly prefer this sort of system over what Google has (if the details described in the lawsuit end up being true).