It seems the deleted entries mainly consisted of Protestant denominations and Pagan groups. They also removed Atheist as a specific religion, and various entries like None Provided and Unknown. Many two-letter codes were changed, which may be confusing if you have groups of soldiers with a mix of old and new dog-tags.
Heathen is yet another term to describe Germanic paganism which has a similar etymology as the Latin originated word "pagan"[1]. It describes the people "of the heath"[2] — the rural folk who were the last to change their beliefs (as opposed to the city folk following the latest trends). English is unique among Germanic languages for preferring non-native vocabulary but the cognate of "heathen" is extant in every other Germanic language to describe pre-Christian belief. Among modern reconstructionists there is no consensus for a term to describe a belief system that never had a name (because prior to Christianity, it didn't need one).
That it is also a Christian pejorative term is irrelevant to the former DoD list.