But does the Red Crescent operate in Catholic nations? Are they even allowed in?
I think that is something worthy of a little more research, but this is my observations. Because islam is so "protective" and applies "the will of allah" to disasters - they have a tendency to keep non-islamic aid away, like the Boxing Day quake/tsunami of a few years ago. Thus an islamic aid agency was formed.
Non-islamic nations are less inclined to decline aid from any source - so it wouldn't be suprising to see Red Crecent at least in partnership with Red Cross if Red C were to get involved. This is partially answered in that another islamic aid group is working with mormons to get aid in.