I don't "use" BCE but I read it with the proper reference. The time division is, just coincidentally, related to the birth of Christ. It is a Christian notation, however you want to call it. I shan't change my usage for political correctness. Now if some different time divisìon were to be decreed, say, the Reign of Hammurabi then I should have to read the notation BH as Before Hammurabi.
As you like it.