What tuned me away from the familiar BC/AD was the knowledge (or concern) that many Jews, Muslims, Hindus, etc., might not like having their noses rubbed into it. ("Before Christ" is probably less provoking that "In the Year of the Lord.")

BCE used to be defined as "Before the Christian Era" and CE as "(of the) Christian Era." Certainly an improvement, since the focus moves from Jesus to those who worship him and write most of the history books. Then it got changed to "Common Era" because maybe just mentioning Christ might offend millions or billions. Not perfect, but better.

Personally I think people should pay more attention to what they do and what's happening around them than to abstract theoretical concerns about language. Most American academics and journalists seem to think otherwise, so I'm ready to go with the flow and be "on the right side of history," so to speak.