Give us a very simple checkbox on each tag, labelled "Show on public shared articles" that would do just that. Show the tag, its reason (and hopefully eventually tag descriptions https://feedback.hudu.com/feature-requests/p/tag-descriptions) on the client's (recipient's) side so that they are privy to the same information we are.
I totally get that some flags are meant for internal only usage in the context of content review and management, but this makes perfect sense in other scenarios.
Good example, same as presented on the tag descriptions request, would be Traffic Light Protocol tags.
If I were to flag a document as "TLP:AMBER", my customer would currently have no indication that they are not meant to share the information generously. Being able to convey this type of information via tags to document recipients would be a huge deal, even further boosted with the new auto-flagging feature.