I enjoy interrupting people who use these to ask them what the basis of zero is. After a little persistence, they will finally state that it is Christ's life. Then I ask them why they insist on rewriting history to exclude an underlying element, would they do this if the time-line was based on Alexander the Great or the first emperor of China?
My ninth grade son's East Hem teacher (who is Jewish) always references dates as BC/AD, in spite of the class textbooks, which use the BCE/CE nonsense. On the first day of class she explained it just as you did, and instructed the students that she expects them to use BC/AD. "I'm here to teach you history, not to teach you how to rewrite history." In a public school, no less.