As a dog owner myself, I want to agree with everyone who says it is annoying and rude and disrespectful to let your dog poo in someone's yard and not pick it up. I curse the people who leave their dog's poo on my lawn, on the sidewalk, or in the park, right along with you! If by chance I get caught out without a bag (forgot to bring one, or it fell out of my pocket, or I misjudged whether the dog was going to go again on that walk and dropped the full bag in a garbage can along the way), then I will scrounge up a piece of garbage (plastic bag, coffee cup, newspaper, etc) to use. Failing that, I have on occasion gone home, got a bag, and walked back to the scene of the crime to clean up. Inconvenient, yes, but the right thing to do.
My opinion about urine on the lawn though, is different. Yes, I try to make sure that my dog doesn't pee on the same spot on the same neighbours' lawns every time, but beyond that, I don't worry about it. Urine is harmless in small quantities - beneficial actually! It has nitrogen in it, which is also part of the fertilizers that people pay good money for. The burning happens only when the dog pees in exactly the same spot time after time. You can also get burning from overfertilizing, or using unbalanced fertilizers. And there are a ton of other things that can cause brown spots in your lawn:
https://www.todayshomeowner.com/how-to-identify-the-cause-of-brown-spots-in-your-lawn/ Is it possible that one of these things is a factor?
I also want to say something about the benefit that dog owners and dog walkers bring to a neighbourhood. Obviously, I'm talking about responsible owners here, not one's that leave their dog's poo on other people's lawns, or those who let their dogs run at or jump on people. We're agreed about those people - they're often not good neighbours.
But people with dogs tend to be out and about in their neighbourhood, and an active busy neighbourhood is a good thing. Break-ins are less likely when there are people around. A dog barking in one yard may even deter a break-in at the house next door. Dog owners also tend to talk to people - we know who lives on our street, and we notice strangers. We notice other things too. I've found, caught and returned lost dogs and lost cats (multiple times). I've found objects people have lost, and returned them to their owner. I've picked up garbage - so much garbage! Especially glass bottles or jars, so that they don't get broken. I've returned garbage cans and recycling bins to their proper house on windy days, or closed the lids so that the stuff inside doesn't blow out. If my dog poos somewhere, and I notice that someone else's dog's poo is nearby, I clean up both at the same time.
One time, I went up someone's driveway, and turned off a tap that they'd left drizzling on the side of their house - there was a huge puddle forming on their driveway, and I worried it would seep into their basement. Certainly it was going to increase their water bill! Another time I noticed someone had left their keys hanging in their door. I took them and left a note on the door (I knew this person, a little bit, from chatting while walking the dog) While walking, I spotted another dog owner who knew the homeowner even better. Turns out she knew where the homeowner worked, and we were able to reach the person at work, and make arrangements for her to get her keys back. I've also gotten to know some of the kids in my neighbourhood, and in my previous neighbourhood. I've intervened when they're doing things they shouldn't be doing - bullying another kid, climbing on the roof of a building, causing property damage, etc. I got to be friendly with 2 elderly ladies in my old neighbourhood, because they used to sit outside all the time, and I would stop to chat for a while on a regular basis. Both told me all the time about how lonely they were, and appreciated the company.
Those ate just a few examples of things that happened only because I was out walking my dog. Sure, I would try to be a good neighbour anyway, but the point is that walking the dog was the opportunity for all those occasions to arise. So maybe try to see your dog owning neighbours in a different way, the responsible ones at least. And balance off the downsides against some of the good that they probably do, even if you don't directly see it. Maybe even strike up a conversation with one of them - who knows, they could turn out to be a good friend!