From the official Red Cross website’s Katrina FAQ:
Hurricane Katrina: Why is the Red Cross not in New Orleans?
Acess to New Orleans is controlled by the National Guard and local authorities and while we are in constant contact with them, we simply cannot enter New Orleans against their orders.
The state Homeland Security Department had requested–and continues to request–that the American Red Cross not come back into New Orleans following the hurricane. Our presence would keep people from evacuating and encourage others to come into the city.
As pointed out at Uneasily Bemused, this seems like an excessively hard-hearted version of incentive management. And before you say “Well, what do you expect from FEMA?” note that the Red Cross attributes the decision to state officials, not federal ones.