I can see it. Personally considering how they say "may he live forever" in reference to the Tisroc, I'd assume some level of influence on the Calormen culture came from either ancient Egypt or Babylon considering that was a common entreaty to the pharaoh of Egypt or the King of Babylon, or the King of Persia, with the former believing believed to be the son of their chief deity Amon Ra, much like the Tisroc being the son of Tash.
Which yes, while Middle-eastern, neither the cultures of Ancient Egypt, Babylonia, or Persia were in the least bit "Muslim".
Now, bringing it back on topic, one major difference between Lewis, and Blyton is the fact that Lewis grants a bit more egency to his child protagonists then Blyton, or Nesbit did. Chief among them is that in Lewis' works the kids are often given weapons to defend themselves, whereas for Bylton, Nesbit, and I'd even add into my reckoning, Lewis Carroll, JM Berrie, and L. Frank Baum, the children just seemed to amble about their adventures with no means of protection against danger. Peter has a sword and shield, Lucy a dagger, and Susan a bow and arrow.