Nah I'm quite the advocate of free speech, and not just selectively so. I think his tweet was ignorant and I disagree with his opinions, but he is entitled to them.
That said, employers have other terms and rules and the BBC has one on impartiality and it does seem that this tax battle may be at least a part of the story, in him trying to define his role in order to pay less tax? Who knows, maybe it's a coincidence.