Of Crosses And Moons

I am no Christian nor Muslim. Heck I am not even a member of the Red Cross Society or Red Crescent Society or whatchamacallit. But this (Photoshopped from mental image) is what I saw on Aljazeera News this morning. The news clip was about Israeli security forces being overly physical with peaceful Palestinian demonstrators:

It seems a right touch compared to:

What would the Society be called then?