The cultural reasons that led to the invention of B.C.E. and C.E. (as opposed to B.C. and A.D.) have no parallel within the Arabic-speaking community. B.C.E. (before the common era) and C.E. (of the common era) were invented as a way to avoid the perceived Christocentricity of B.C. (before Christ) and A.D. (Anno Domini, or "the year of our Lord"). The polarization that exists in the Western world between Christians and the secular movement has no parallel in the Arabic-speaking world, the majority of which are Muslim, who, as it happens, do not find it offensive to use a calendar that refers to the birth of Christ. After all, it is only one calendar available along side a Muslim calendar that refers to the flight of the Prophet Muhammad from Makka to Yathrib. The Arabic expression does not refer to Christ as "our Lord" and, in most cases, does not even mention Christ, although the "Birth" is understood to be the birth of Christ.
So the terms B.C.E. and C.E. need to be localized to their cultural equivalents.