I can see where you are coming from, but I don't think you understand - in the slightest - what refereeing kids is like.
On the one hand, we are aware of a duty of care for safety. On the other, we all would like to see a good game of rugby (continuity of play and fair contest).
Speaking for myself, I do not care about who wins or loses, and I do not even care if I make howlers in law, but I do care that kids or for that matter any adult players - including pros - don't get serious injuries. I therefore also care - when I am not refereeing, but discussing after the match or online - about the example pros or other adults give, on TV or simply in a club situation.
That said, if a parent comes round after the match - however politely - I am not interested in them trying to "ask a question". Not because I have an arrogant defensive approach, but because it adds no value whatsoever. If I made mistakes, I will reflect on how to do better, but I don't need a parent to help me to do that.
I found myself nodding at everything you wrote..until the last part of the last sentence.
If you are thinking that parent is trying to 'help you reflect on your errors' then you are being defensive. If you were to explain to that parent just what you explained in the rest of your post I daresay you would get that very message through to a significant portion of them and help change attitudes.
We all know that parents can get way too involved in their kid's sports, but surely communication will change attitudes far better than rules or non engagement.
I fully respect anyone's right to not engage in a post match argument, and I also fully expect team management to support you if someone goes down that path and you choose not to engage.
What I am suggesting is that if you have a pre-ordained attitude of not engaging then this only serves to widen the gap between the referees and the remainder of the game.
Maybe I am overly optimistic regarding behaviour but I can tell you that many parents/ players etc would love to hear what you said in the first part of your post and be totally accepting of that. Instead they just think you are being aloof (or worse).
It is an ingrained problem right across the game and even worse at pro level where trial by media is par for the course.
You do a great job being out there refereeing. Be proud of that and own it. Be part of the game instead of being a game in isolation with other refs.
I really feel for the refs I see turning up to games by themselves then wandering back to their cars straight after by themselves again because they aren't included or want to avoid possible confrontation. Rugby isn't (or shouldn't) be about that.
Sometimes those other folk want to talk to you about things that happened in the game because they are actually trying to be inclusive. I'd love to see clubs and schools be more inclusive with refs and drive behaviour around it as well. FFS, if we can bash the crap out of each other on the field as players, then have a drink together after, surely we can do the same to the ref.
It takes two to tango though.