A week ago a bank in the building my wife works in posted a sign "We will be closed for the winter holiday". Now their sign reads, "We will be closed for New Year's Day". If naming Christmas is unacceptable in today's multicultural world then why is New Years acceptable? It is not the Chinese new year nor the Jewish new year nor the Islamic new year. They all have their own calendars and numbering systems.
Until recently we expressed the date as AD for "amno domini" which is Latin for "year of our lord" based on a calculation of when Christ was born. Dates less than zero were "BC" for Before Christ. This has been relabeled "common era" so tomorrow night we will celebrate the start of 2012 CE.
The modern calendar has a lot of the same heritage as Christmas. The date for each came from Roman holidays. It and the Catholic Church are the two main Roman institutions continuing in the modern world. The current calendar was created by Pope Gregory XIII. Because it was seen as a Catholic calendar it was not adopted for centuries by protestant countries (England adopted the Gregorian calendar in the 18th century, Russia and Greece in the 20th century).
The Gregorian calendar is the most accurate in general use which is why it is the unofficial standard for the world but it is still tied to Christianity and Europe. You would think that it would be just as culturally insensitive as Christmas which is celebrated in many non-Christian countries (China and Japan to name two).
Maybe I shouldn't be pointing this out. I could start a war on New Years.