I would heartily agree that the Gregorian calendar is
very much a Christian creation. Named after the Gregorian Monks.
I honestly would prefer something based on a shared solar event. The Crab Nebula and supernova in 1088 ACE would be a good neutral place, as would other events, like Halley's Comet.
It would be secular, and sold to the world as such. But it would put the focus on solar events, in which any number of peoples can use as an omen for their local system of religion and symbolism. Can't win everything here, but neutrality is certainly a laudable goal.
(Edit: wow, quite a bit of -1's, and no real good reason why. I was hoping for a good neutral dialogue, rather than bemoaning current date systems. And also, it may have been Pope Gregory. It still is bound to the Catholic church.)