He's a presenter reading an autocue so his personal views shouldn't come into it and shouldn't matter. If he attempts to vocalise them then his employers should point out he is representing the BBC not there to represent his own views and take disciplinary actin if necessary. If they didn't I think it would be this that would effect the BBC's reputation.
While that is broadly true I think the Breakfast programme is more 'conversational' than, say a standard news bulletin, and therefore has more opportunity for the presenter to stamp their personality on the role, and that might include their own personal views.
The BBC should be careful about ensuring that his creationist views (which are indeed extreme) aren't promulgated on the programme - even is a rather 'soft' way in a manner that would affect impartiality.
This isn't the only headache the BBC has over impartiality - there is currently a debate waging over the team of senior political correspondents and presenters, who seem to be disproportionately right wing and often from exactly the same elite group who currently run the country. Concerns have been raised over Nick Robinson getting the role on the Today programme.
Also the rather odious chummy, chummy interview of David Cameron (in his kitchen) before the general election by the BBC Deputy Political Editor James Landale which came across as if they were old school chums ... until you realised that they were old school chums.
The BBC needs to take care.