Was neighbour BU?

Indeed it should. But equally, the people not answering the door don't know what the knock is for, so shouldn't be judged for not "according the respect" for a request they didn't get because for one (perfectly valid) reason or another they were not able to come to the door.

I would open the door to a neighbour, but if I didn't it would be for a reason. Maybe I was doing something and couldn't come to the door in that moment, or maybe I was on the phone, or whatever.

Classic MN response (by others, not you OP!) that there is no such thing as a community, empathy. I've been in your position, and your neighbours' position, and not once did it cross my mind that making such a request, or acceding to such a request, would be unreasonable. Pets are not flowers, they are important and someone looking for a lost one should be accorded the respect such a minimally intrusive request involves!

An observation, OP - while I haven’t read all the comments, I’ve noticed that you’re arguing with a lot of people.
That automatically makes people angry and sets them against you.
Just a thought.
Did your neighbour know it was you? Because I don’t see how they could be unreasonable by simply not answering their door. Maybe they were eating - we used to eat that late when my dad got home from work. Maybe they were having sex - did you think of that? And maybe, just maybe, they just didn’t feel like getting up and answering the door - completely and totally their right as homeowners.
I’m sure had they known it was urgent they would’ve hurried to the door for you - but nobody is a mind reader, all due respect.
I’m really happy your cat is okay. Our pets are incredibly precious to us.

I'll be showing up at your door tomorrow. Will you answer?

It does sound like you might be using the cat to fill your empty nest a bit. Unfortunately cats are a bit like an 18yr old. They will randomly decide to stay out all night, then moan at you because you weren't there to let them in at 3.05am when they got the munchies. They will sleep most of the day. If you try to show them affection they will look at you like you have come from another planet, yet if they want affection you would be unreasonable to refuse it. They will treat your house like a hotel, all inclusive of course. They will however think nothing of going around to a mates house and eating at their house then still stroll in wanting more food. They will get in scuffles with their mates as they establish the pecking order. They would quite happily ditch you entirely but they can't be bothered to support themselves so tolerate being around you for the food, shelter and affection on their terms.

I did google it OP out of interest. This is what I found out:

No, answering the door is generally not considered a value judgment in a philosophical sense. Value judgments involve opinions about what is "good" or "bad," "right" or "wrong," or "ought to be". Answering the door is a simple action with no inherent moral or ethical implications.

While you might have reasons for answering (e.g., politeness, expected behavior) or reasons for not answering (e.g., safety concerns, privacy), these reasons themselves are not value judgments.

YABU to let your cat out at 8:30pm to play out on its own with no supervision and no tracker. Are you near roads? Some drivers deliberately drive at cats. I believe cats have the equivalent IQ of a 3 year old child. Would you let a toddler out at that time?

That's fine, we can agree to disagree 😉

I would also answer the door and look for your cat OP if I wasn't busy doing something else which prevented me from coming to the door at the exact moment you rang the bell.

Yes, I do know the difference between fact and opinion. You don't need to write in capital letters for me.
I also know this is not a value judgement, as the previous posters have explained to you.
You are being unreasonable again OP.

Ah I think you are getting a very undeserved hard time on here @BarbarellaC I’ve had cats forever but was still way worried when my 2 12 month year old sisters went out 2 yearsago

i've knocked on neighbours doors houses twice during the day in that time. Especially the early days when new patches were being agreed and there were lots of noise going on

i work from home and try and get them in by 6 at night but really struggle on the long days. Empty bellies and Dreamies do help

I would answer my door to you and look for your cat @BarbarellaC ! And I’m in the sticks!

8.30 is dinnertime for us. I would not interrupt my dinner to answer an uninvited doorbell, and if I did and it was someone wanting me to go out to the garden to check for their cat I would be disinclined to help.

If the cat had been missing for a few days and you came at a sensible time (as some neighbours did recently), I would be happy to check (well, I sent one of my dc, no way was I hunting around for anyone else's cats when I don't do it for mine!)

I made pizza tonight for tea. I had no pineapple in the cupboard so I made a value judgement not to put pineapple on the pizza!!!

If your imagination fails you, you can read this thread as there are many many reasons given why someone might not answer the door at 8.30 or anytime. None involve shaking behind the sofa interestingly enough. Although social anxiety or agoraphobia may prevent some people from answering the door but I don't think that has been brought up on this thread yet.

🙄

Like a pp on page one, my first thought was they were having sex or just somewhere in the house where they don't hear the doorbell, or watching a loud movie or all of the above.