I think OrphanCrow is on the right track. They probably want to know the race so that if it's a minority they can get an elder who belongs to the same minority, on the committee to head of any future allegations of racial discrimination.
I also saw an application form for attending Ministerial Training School that also asks the applicants race. I think the reason for this is to ensure they can control the ethnic diversity on the campus so that they can always engineer the outward appearance of racial tolerance and diversity by having a mix. They big on outward appearances and creating a spectacle of love and peace and harmony for "the world" to see.