VIRII said:
I would expect to get short shrift if I went to the police station and refused to deal with a woman or black officer. Rightly so.
No-one said anything about anyone refusing to deal with an office of different sex or ethnicity, simply that it was and is easier to deal with people to whom you feel you can relate though cultural, ethnic and gender similarities.
Let's try a different tack:
Humans are naturally tribal. Everyone is, whether they choose to admit it to themselves or not and in most cases they prefer to associate with 'similar' people; when I look at my wedding photos I realise that out of 180 guests there was 1 black person and 1 oriental person, everyone else what white caucasian. Why?
I live in London and associate with numerous people of different ethic origins on a daily basis, I spent 8 years at university in a multi-ethnic / culture environment where mixing was extremely positively encouraged and yet just over 1% of the people invited to my wedding were non-white.
Personally I think that it's because I have very little in the way of shared cultural reference points with people from other cultures; we weren't raised the same way, we don't laugh at the same jokes, we don't follow the same sports, watch the same TV shows, listen to the same music, wear the same clothes, generally we have little in common. It's not deliberate racism, it's just that I enjoy the company of people who have similar cultural reference points to myself and I feel comfortable in their presence. After all, you don't go for a night out with people who don't make you laugh or you can't hold a conversation with (at least not on purpose). As a prime example of this in action; you can't understand what I'm saying in this thread because you don't know me, my cultural reference points and we have no shared semantics.
The reason the two people from miorities were at my wedding was because they had both been educated in public schools (boarding) and so they were more immersed in our culture and their likes / dislikes and behaviours were more compatible with my own.
Now apply this on a larger scale to minorities dealing with the police; it's easier and more confortable communicating if you have a shared cultural identity and shared semantics. Hence having a ethno-cultural diversity that matches that of the public will make it easier for the police to go about their business.