The goal of these scholarships is to turn college campuses into a mosaic of people from all different backgrounds. They're also intended to even the odds for people who have traditionally had more difficulty going to and affording a college education. While it's beneficial for those coming from such backgrounds, for those (generally white males) who don't qualify for such scholarships, it can feel unfair.
They don't use the term diversity lightly, though, and in some areas this can actually work out to your advantage. If you're a high schooler looking to go to college, in places where white students are a minority you actually may qualify for a scholarship. This generally means attending a historically black college. While an impressive list was given in this article on the subject, whether because of poor website design or an actual lack of the scholarships, searching myself I was only able to find a couple. I was able to confirm, though, that Alcorn State University in Mississippi does indeed offer a diversity grant to non-black students. Mississippi State Valley University also offers a diversity scholarship, but does not disclose its details.
Scholarships like those, however, are few and far between. Your best bet is to express this disadvantage when applying for other scholarships. I can't emphasize this enough - when you mention that your status has been an obstacle in your scholarship search, do not be bitter or self-pitying. That won't earn you anything. Instead, perhaps mention somewhere within the essay that you don't qualify for many other scholarships, and that it is therefore even more important that you earn the particular scholarship you are applying for. To be safe, if you do use this argument have an adviser or adult read over it first, to make sure it came across right. If you play your cards right, the fact that has made you unqualified for many other scholarships may well increase the likelihood of you getting another. Scholarships are out there to give money to those who need it, and if your status means that you don't qualify for other scholarships, logically that means that you need their scholarship even more. However, since I'm not in the position of not qualifying for diversity scholarships, this is untested territory, so be careful with the way you phrase what you write.