Apparently the issue of non-Christians celebrating Christmas was not merely a modern Western phenomena. Philip Jenkins’ book on Middle Eastern and Oriental Christendom quotes one source that recorded:
“Christians, Moslems, Jews and Nuseiriyeh [Alawites] visit each others’ shrines. The Moslems take their insane, or “possessed” to get rid of their evil spirits in the cave of Saint Anthony… Christians go on a similar errand to the well at the shrine of Sheikh Hassan er Rai… During the procession on Good Friday, barren Moslem women pass under the cloth on which is stamped the figure of Christ, in hopes that they may bear children. Nuseiriyeh observe Christmas, though they subordinate Jesus to Ali… Instances of Moslems seeking baptism for their children as a sort of charm have been reported from all parts of Syria and Palestine.” -American Archaeologist in 1912 (in Philip Jenkins. “The Lost History of Christianity” p. 205)
In India similar things took place where Hinduism provided the relativistic framework for such liturgical plurality and hotchpotch. The Nuseiriyeh were an arabic syncretic religion that blended Islam and Christianity, so their celebration of Christmas makes sense. This reminds me of one incident where a Muslim classmate of mine corrected me on my claim of the separatist attitudes of Muslims when she told me of medieval precendence for Muslims allowing Christians a mosque to worship in, which I was surprised by.