The Blue Sky moderation service is 100% optional and adjustable by category. The option for them to hide "intolerant" posts in my feed is entirely disabled. As such, when I go to the Babylon Bee feed, I don't see intolerant moderation labels at all. The content is all completely visible with no mention at all that a label was even attached.

You're complaining about something you have near zero knowledge about. The rage bait your twitter feed fed you is proving to be very effective.