I'm not sure entirely where you are getting the 50% number from (source?) but it is true that the Abbasid Caliphate included a very large population of non-Muslims. As you can see from this map the Abbaside empire included a number of dynastic groups at that time--there were many non-Muslim groups in both the far east (including India) and in North Africa. It also included considerable populations of Jews and Christians.

I believe that factoid comes from a paper by Richard Bulliet called "Conversion to Islam in the Medieval Period: An Essay in Quantitative History", involving something called "conversion curves". I haven't read it, but here is a link to a non-free version of the paper.