This is the subjunctive, a very formal construction in English, more commonly used in AmEng today than in BrEng. When a compound sentence or a main clause begins with "be" the subject must follow, and this may take the form of a subject pronoun. In the OP's example it means whether… or not.
… be they good or bad
… whether the news-worthy stories are good or not.
You would not use the object pronouns (him, her, or them) but you could use a determiner. As the following phrase is an idiom, we cannot substitute "that" without changing its meaning.
be that as it may…
Building a new children's home will cost a lot of money but, be that as it may, there is an urgent need for the facility.
Cambridge Dictionary
There is a famous children's story called Jack and the Beanstalk, and these lines are snarled by a giant.
Fe, Fi, Fo, Fum.
I smell the blood of an Englishman,
Be he living, or be he dead,
I’ll grind his bones to mix my bread
Nowadays, especially in BrEng, we'd say "If he's alive or dead, I'll grind his bones to make my bread."