In the post-trump era, right wing complaints against an organisation aren't necessarily a sign that that organisation is doing a good thing. Complaints from the factions in power in the UK at the moment are usually just a sign that their actions 'arent right enough' rather than not being right wing full stop.

Also, the BBC News wing has separate management, some of whom were appointed during Cameron's time in office. So the drama and comedy produced by the BBC can be independent of its news editing.