This makes more sense to me.  Mirv's comment is confusing to me...the Christian God is never lowercase either...the English equivalent of a lowercase-g god is, well, god.  So, will we say "Christians believe that their god, God, does X" or "Christians believe that God does X" (with perhaps an intro explaining who this "God" is)?  I much prefer the latter.  I trust no Muslim would want the sentence "Muslims believe that their god Allah does X", but would prefer a brief intro explaining who Allah is, followed by sentences like "Muslims believe that Allah does X".