Well, likely he wouldn't, but we can be sure that he would reject someone outright for having "President of the European-American Student Union", can't we? Charitably, this is because there is essentially no chance anyone would ever file a lawsuit for rejection of the second candidate. I'm sure you can draw the uncharitable version yourself. :)
It's both wrong and illegal to reject a candidate based on their race, regardless of what race that is. And I am pretty sure the OP was not implying otherwise. Further, I assure you that white people file discrimination lawsuits too.
// Out of interest have you a reference to a white person winning a race discrimination case, preferably with regard to being hired?
Also why should "an applicant who had 'President of African-American Student Union' on their resume because it belies their race?"? Surely a person of any race can be president of the African-American SU, or are they allowed to be racists?
http://www.dailymail.co.uk/news/article-1077466/London-Under... is a case of failing to protect a white worker from bullying whilst at the same time being extremely protective of black workers.
Just FWIW.