"The simplest reason for using BCE/CE as opposed to AD/BC is to avoid reference to Christianity and, in particular, to avoid naming Christ as Lord (BC/AD: Before Christ/In the year of our Lord)."
That's not correct. The reason CE and BCE are used is because Jesus was not likely to have been born then but more likely around 4 BCE or a bit sooner. Instead of redoing the calendar, which would be impossible, a more neutral term was used.