Equal Opportunity Employment jobs and the "non-Hispanic" selection

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Of late I have been trying to get a job, and a majority of the places I have applied for had on their website (or elsewhere) written that they were equal opportunity employers (meaning they do not discriminate, practically on all superficial grounds). Now my question is, is it possible for a company to truly live out this promise? I have noticed, primarily over the past year and a half, the rise of "non-Hispanic" origin selections on applications. What does this really mean and imply? And what is its purpose? I am beginning to wonder if the fact that I am white is diminishing my chances in the field (I am only looking for a part time, minimum wage job; so it is not like there is much experience necessary). Is it just me or are the racial grounds for employing someone kind of touchy? Some companies even need to fill a quota (so to speak, for lack of better words) on how many people from different races are employed. Does this not break the equal opportunity rule? If a company can not hire a white person because there are too many already working at the company, is my opportunity diminished? To add, is it things like this that keep maintaining racial tensions? Why is race so important in the context of hiring someone (and maintaining a company)?