My mum is one of these, embarrassingly.
Firstly, you won’t change their minds with logic. And you might not change their minds at all- some people just need to feel hard done by. It’s really hard to feel like someone doesn’t like you, but try as hard as you can to remember it’s a them problem, don’t let it get under your skin!
I’d ignore it as much as possible though - don’t answer the door to them, don’t engage in discussion, don’t offer ‘compromises’. Chances are any compromise won’t work anyway, they’ll just find a new thing to be upset about. If they nab you and complain, say very little other than ‘oh’ or other totally noncommittal niceties, get out of the conversation ASAP and DO NOT CHANGE YOUR BEHAVIOUR so they don’t get results from their complaint. This is key.
If you WANT to do an occasional nice thing for them (dropping off extra baking, asking if they need anything at the shops if you see them on your way out, offering to feed pets if they’re going away or whatever) then that MIGHT over time get them to see you as a ‘friend’. Some people, once you’re a ‘friend’ it’s all good, but with others that will only last until they find a new way to feel upset by you so it’s really up to you how much energy you want to devote to it.
Also a massive apology to anyone dealing with neighbours like this, their adult children are very aware it’s absolutely horrible but sadly there is, it turns out, fuck all we can do about it!