From their HFC Editorial Style Guide:
So evidently BC and AD are a big no-no with the NPS. They never say why. But this is what they say at the beginning of their style guide:
References often disagree—that is why style guides exist—and questions of style must be decided with the public foremost in mind. This is the audience for whom National Park Service public media are produced, not scholars, historians, scientists, or bureaucrats. It is important that the editorial style used throughout your publication, exhibit, web page, podcast, audiovisual production, or other media be consistent.
Yeah, you and your friends and everybody you know uses BCE and CE, right? Sheesh . .
Here's their Contact Form if you want to tell them how you feel.