Initially reported in this comment; spinning off to handle separately.

Following description is from @trichoplax:

In my development environment, I took the following steps:

1. As an admin, make a tag moderator only and add it to a post.
2. As a user, try to edit my own post to remove the moderator only tag from that post.
3. As that user, see a red warning message indicating I cannot remove a moderator only tag.
4. Notice that the post no longer has the moderator only tag.
5. Go to the post history.
6. Notice that the latest edit is the one adding the moderator only tag, and there is no edit showing the removal of the moderator only tag.

Further local development environment testing

I took the following steps for the post that lost its moderator-only tag in the previous testing:

1. As the same user, make an edit to the text.
2. Before saving, notice that the moderator only tag is present in the relevant edit field.
3. After saving, notice that the moderator only tag is present again.
4. In the edit history, notice that the latest edit shows the moderator only tag being added (by the user).