I don't know this from personal experience, as I've never worked for a large company like that, but my impression is that if you were (part) black, Hispanic, Native American, Pacific Islander, etc., it might be an advantage to you to disclose that fact, in case the company has some type of affirmative-action policy in hiring that would give you a slight edge over other candidates. If you're Asian, however, that's probably not the case, as there tend to be more than enough Asian applicants.
Seen from the broader picture, your individual disclosure enables the company as a whole to keep statistics, as dude says, and be sure that they're attracting and hiring enough minority applicants. That might not benefit you personally, but if you see diversity as a value worth promoting, minority participation does benefit the company, and even society as a whole. That's essentially the reasoning behind the whole concept.
Apart from that, however, I agree that there ought not to be any disadvantage in not giving that piece of information, and I think you're right to do what seems right to you, in keeping with your personal ethics. If the company is large enough to advertise job openings in Europe, their HR department ought to be aware that especially German speakers have a very different historical perspective, and probably most of them feel as you do.