AD and BC should not be replaced because while we do live in a secular society, and while the terms are religious in nature, the calendar we use is based upon and revolves around the time of Jesus - a religious belief. If you want to replace BC and AD with secular terms then why not replace the whole calendar? If we stick with this calendar so too should we stick with the terms which reside alongside it.
Yes, BC and AD are terms that effectively communicate when a date took place, relative to human history. The purpose of the designations are only to communicate historical facts in relation to time and date. The terms BC and AD have done this effectively for thousands of years. BCE does not mean anything, and thus it is no more correct than using BC.
Since we live in a secular society it is not appropriate to use religious terms to refer to scientific things. BC and AD are Before Christ and Anno Domini, basically religious terms from Christianity, that have found their way into everyday life. The scientific alternative BCE and CE, or Before Common Era and Common Era, are more appropriate for teaching and scientific use. If churches prefer to stick with the old BC and AD, that is their right, but schools should use the scientific terms.