Considering LB reveals that Tash is real but (unlike, say, the ancient Greek deities and most of the Hindu ones) is not exactly humanlike — from the descriptions in the book, he's much bigger than a man, has a vulture's head with a cruel, curved beak, and four arms with claws for fingernails, and gives off a foul smell like something dead... ummm... well... let's just say I can't imagine very many human women — not even members of the Calormene royal family — lining up to have his babies.  

So I would say it's almost certainly just a myth conjured up to boost the status of the Calormene rulers and their relatives. Unless Tash can take other, somewhat pleasanter forms at will. But we've got no indication anywhere that he can (unlike Aslan, who is definitely able to appear in different forms even within Narnia, let alone in other worlds such as our own), so I'll stick with my conclusion.

I believe it's the same sort of status claim made by the ruling classes of ancient pagan civilisations. Reciting their genealogy back to a god certainly sets them apart from the ordinary peasants they lord it over.  

I'm thinking of Aztecs or Incas. 

[On the other hand, Jesus' genealogy goes back to Adam, who is described as 'the son of God', not because he was divine but because God made him.]

Posted by: @coracle

I believe it's the same sort of status claim made by the ruling classes of ancient pagan civilisations. Reciting their genealogy back to a god certainly sets them apart from the ordinary peasants they lord it over.  

I'm thinking of Aztecs or Incas. 

I believe the Egyptians had the same system. It was important for a Pharaoh to marry his sister, to keep the bloodline pure.

There's no indication that the Calomenes kept that part of old traditions, though. They seem to have had their own mythology.