This is exactly the problem. The BBC has a duty to provide balance even if one point of view is clearly less credible than another. They are not allowed to editorialise.
They are allowed to editorialise, and frequently do - look at the difference in outlook between Andrew Neil's descriptions of The Mash Report and their response to it. Collectively, the various elements of the BBC shouldn't favour any given agenda, but they do have an obligation to truth and accuracy.
The problem is that balance doesn't mean giving equal weight to each side of any argument, because the arguments on various sides do not have equal validity - that was the conclusion into the review of the coverage of climate science and the rebuke by Ofcom that was given to Radio 4 for continuing to listen to Nigel Lawson's fabricated nonsense on climate changes. Balance REQUIRES an editorial judgement, that's why it's the editorial choices that make the Daily Mail and the Guardian have vastly different outlooks, how the BBC manages to offend both sets of readership on a regular basis. It's also how the mere existence of 'codes of conduct' on the likes of Facebook and Twitter, which are editorial codes by another name, belie their claims to be 'platforms not publishers'.
O.