Economic diversity, racial diversity, and religious diversity all spring to mind.

EDIT: Downvotes? For this?

I'm not claiming that lacking the diversity is a good thing, merely that having extra options decreases cohesion. The more diverse the economic situation is (say, due to vast wealth inequality) the less cohesion there is. The more diverse the religions are, the less common-ground people have based on religion--as in most of European history. The more racially diverse a place is, the more tensions due to race (LA versus Helsinki).

Is it worth the hit to cohesion to have better diversity? I'd argue that, in the absence of external threats, it absolutely is. But living in a fantasyland where diversity doesn't come at the expense of cohesion doesn't help.