I think its very common in most countries for public broadcasters to lean left, and there is nearly always the perception. In my experience this has always been true.

It might be because a right-wing government is more likely to make cuts in funding of a public broadcaster than the left. I have not thought the reason why it is in depth though. I wonder if you have an opinion?

I wouldn't say that its an unreasonable theory. There's also the tendency for those working in media to be of the left. My main point though is that any perceived bias comes from the individuals that happen to be working on that production. The organisation itself is non-bias and has many measures to avoid bias.

In general conservatives seem to be more close-minded. It makes sense, really - they want to keep things the way they are. Liberalism on the other hand encourages introspection and change; informing oneself is a necessary part of that. So, those that distribute information are likely to be less conservative. You see the same trends in technology and science in general.

Note that this is not an absolute endorsement of liberalism; change can only be positive if people are properly informed, and doing it for the right reasons. And, well, they aren't - not for some time now. And it's been hijacked by identity politics (some is very good; some very bad, more to do with narcissism than anything else, sigh)