If I could wave a magic wand and give gifts to Baghdad (to share with environs of course), I'd probably put the following under the tree: Office and Home Depot outlets (substantial ownership in both chains, including stateside), a SeaWorld (Iraqis choose the site), lots of steady, cheap electricity (they can certainly afford it), membership in Costco, a new science museum (like OMSI), Netflix.
These gifts would be delivered irregardless of religious affiliation or sexual orientation.
In the USA, Xmas is a commercial/secular holiday, on which religions piggy-back. Jesus was not likely born on December 25 and in any case the gift-bearing Magicians showed up later (ritually on Epiphany, January 6).
The USA traces its origins to many Roman institutions (evident to anyone visiting Washington, DC), including Saturnalia. None of which is to say there's anything wrong with Christians piggy- backing on our secular holiday, as long as they don't mind sharing it with the rest of us.