If trust of one's own race is lower also, this seems unlikely to be a consequence of ethnic diversity per se. Rather, I would speculate that, due to the tendency of people to group with their own race, more diverse neighborhoods simply tend to be more transient neighborhoods - places where people are "just passing through" and not really there by choice. There is no point attempting to build community bonds in an area with high churn, and that you yourself plan to move out of at the soonest opportunity.