I thought it was because Bannon is the subject of the article in this case, anyone else would be subject to an honorific? Perhaps, maybe?
Additionally, Trump is ambiguous, could refer to a whole family of people with varying social standing.
Sidenote but ironically BBC News is a terrible reference for good written English, you’d think it would be, but no.
I was surprised to see that BBC News uses them at all actually. I haven’t regularly read the site for years, but courtesy titles aren’t used in many other publications (e.g., those conforming to AP style).
It’s not this, at least not primarily. Including “Mr”/“Mrs”/“Miss” reduces ambiguity marginally at best (it would only affect any articles also discussing some female Trumps). In any articles discussing multiple family members/people with the same family name, the writer would need to make it clear who’s being referred to in each case in some other way, e.g., by using their first name or the context.