>>If society was secular, would Christmas be a public holiday? But not Hannukah, Eid , Diwali, etc?

Yes - it will be since it being part of Millennia  long tradition it has inevitably intertwined in the social fabric of Christian based society. 

And secular societies, based on Christian culture, have bet backwards accommodating the other cultures, to a point that you don't get to put a  Christmas tree, or  issue a "Happy Christmas" greeting in offices anymore.