On a tangentially related point, I attended a Christian private school where we were taught that it stood for Common Error, rather the Era, and that it's was somehow a diabolic plan to subvert Christianity. This among other reasons us probably why I am now an atheist.
Small point, consistent use of BCE/CE is preferable mixed usage or use of BC/AD. Thou shouldst not cross the streams... https://en.wikipedia.org/wiki/Common_Era
BCE/CE is preferable to BC/AD in all cases.
No it is not. BC/AD has been in use for hundreds of years and is just fine. You can use BCE/CE if you want but it is no more valid than BC/AD.