I agree with your sentiment, but you’re in error here.
B.C.E. does not stand for “Before Christ Era”. It stands for “Before the Common Era”. C.E. stands for “Common Era”.
Obviously what made the era “Common” was the Church, and that was founded by Christ, but the “C” stands for “Common” and not “Christ”.
Progress.
Now why was AD CE changed since they are identical?
If Jewish scientists wanted their calendar, they would call it AM/BM, After Moses or Before Moses.
Same with Muhammhed or Buddha.
If Atheists want a calendar, pivot around a star event, a supernova, because defining the modern era is tricky.
Conservatives keep saying they must grab the popular culture from the collectivists.
When I do grab the culture, by calling CE the Christ Era, it is the Conservatives who piss on me. Hypocrites.
But do not piss on people, and say it is raining.
CE is the Christ Era pivoted around the Christ event.
I took the culture back.
So, put that in your pipe and smoke it.