The alpha radiation that DU emits is not strong enough to penetrate human skin, so just being near depleted uranium is not a health risk. But it may become a health hazard if it is ingested or inhaled, or shrapnel fragments are retained in the body.
It's really just one more hazard a former battlefield can have. If I was in or around a former battlefield that had DU rounds used, I would be more concerned about unexploded high explosives.