Goodall, as always, misses the point. Yes, the BBC gets criticisms from both right and left (and I know sex/gender doesn't fit neatly into this, but in BBC groupthink the GC position is right coded). He should be asking himself why it's criticisms from the right that stick.
Criticisms from the right are usually, not always, about content, like splicing together two Trump quotes to make him say something he didn't say, or giving undue weight to statements from Hamas, or only covering trans issues from an "affirm and celebrate" perspective.
Criticisms from the left tend to be much more vibes based, like Laura Kuenssberg isn't explicitly left wing, or Nick Robinson did a hostile interview with Corbyn, or Farage is on QT too often. The complaint is that the BBC isn't biased towards them.
You also get a sense of this with ex-BBC types who start podcasts, where they aren't bound by a corporate line any more, and they can express their opinions, and it turns out they all have more or less the same opinions, and exactly the opinions you'd expect.
I'm sure Goodall thinks he's an independent thinker calling things the way he sees them, and it never even crosses his mind that he's a regime mouthpiece. That's how bubbles work.