For some reason, nobody complains when they have to fill out the paper equivalent of these web forms. I did, and happily indicated my race too, in a whole room full of people at my company, and nobody was complaining. I think that we're used to filling out much shorter forms on the web, so seeing a long form with a lot of fields there is disconcerting, but the quantity of information they're asking for is on par with most other paper forms I've filled out.

Also, we don't live in a world where DNA sequencing is free. Seems like common sense to fill out your race.