IIUC it's because the BBC has had some dabbling with transphobia. A few admins are inferring that their Mastodon moderation policies will be similar to their editorial practices so it's just a matter of blocking yet another instance that has a mismatch in moderation policy.

Business as usual on Mastodon, that's why it's decentralized in the first place. mastodon.art users who want to participate on the social.bbc instance can just go do so using another instance.

If you read the linked thread, it's because of the BBC's increased bigotry toward LGBT+ people over the past few years.