If it doesn't matter and it's such a tiny thing, I am surprised that folks don't come up with the use of the Islamic dating system, which certainly would please many folks. This would be, what?, the year 1400 something, wouldn't it? We could adopt the Hebrew calendar, which has the advantage of being much the oldest, though all those lunar calculations would drive me personally a bit to distraction. The problem with any of these, is, of course, that they promote some sort of religious conflict, which will be pretty much denied by proponents of the faith advancing their position.
The default position is to use the calendar that's more or less become the standard, but to try to take away the cultural imperialism that other religions and folkways tend to experience when they have to take another of those western Christian forced feedings that they are periodically required to grim and swallow as if there was nothing unusual about that. For the Western Christians, or at least many of them, there is nothing wrong with that; everything is the way it should be.
Occasional Westerners who may be Atheists or Agnostics or non-Christians of one sort or another will be familiar with the feelings that I speak of here. Others may be shaking their heads in complete and stunned bewilderment. There is, if fact, nothing wrong with taking an arbitrary Christmas as the beginning of year One; it simply works better for everybody, as opposed to simply those folks who are Christians, to think of it as the time we all agreed to start counting together; or, for Goodness' sake, The Common Era. The time that nobody's really figured a classy way of describing that happened before that, well, Gee, Before The Common Era seems good enough for Government work.
It's probably the least upsetting alternative for the whole bunch of us, as opposed to selected bunches of us taken one at a time. Of course if you really need an issue to make things more difficult than they absolutely have to be, and to cause resentment that really doesn't need to be there, feel free. I always thought that C.E. and B.C.E. sound a bit labored anyway, having only been introduced to them when I was about eight years old, and used to the B.C. and A.D. already. I still think, though, that despite their awkwardness, they are, for the reasons I spoke about above, better.