Thank you for this post.
Sometimes kindness is painful. For example, a doctor amputating someone's limb to save their life. But of course, it is nice if it is as painless as possible. In the case of that woman, I think you went the overly painful way, but I can see your intent was not to harm. I admire your ability to admit your mistakes.
As for necessity, I follow this rule: if I say/write something publicly, I should be ready for criticism. If I don't want it, I should stay silent. The same works the other way: I can criticize anything I want (while trying to be nice and properly proving my point) if it was shared with me. So, in case of your friend's post about monarchs, I see no problem. It is his property, but he has let you in, allowing to comment on his thought. It's not like you came to his house and started throwing garbage all around. Also, it was not even something personal for him, unlike, for example, religious beliefs.
Although, I agree that sometimes preserving good relationships is more important than proving someone's wrong.
Well-stated.