It amazes me how neighbours allow petty matters to dominate their lives. We all have to get along, otherwise it's just a big pain and wasted effort in the long term.
I'm lucky, I have good relations with all my neighbours. I regularly cut the grass for the old girl next door. I voluntarily patched the other neighbours fence this year. I've filled a pothole in our shared driveway at no cost to them but myself. Of course, I walk on water in their eyes now but it's important to me that we maintain a good community in our little corner of the world. It certainly means I don't have frosty neighbours come shouting at me and making demands of me like op has.
Quoted for truth, I live on a corner plot so only have 1 actual neighbour ajoining but she's a 84 year old lady and yes she gets a little bit tiresome but honestly could be a lot worse (she's also quite ill at the moment been in hospital 2 weeks).
Like yourself I've cut her grass before and done other odd-jobs for her and when we were having our kitchen replaced she had us round for tea as we couldn't cook anything, certainly makes for a more peaceful existence.