Adding to the above as a former dog trainer, shelters do not always have the resources to test a dog in EVERY conceivable scenario in a less intense environment. They are adding these notes so you dont see a dog like in the og image and go "Wowwie! I'm gonna take him home and turn him loose in my house that already has an established dog who owns the space!"
Some dogs that are reactive are only reactive in certain scenarios. Some are reactive only to certain dogs. Some are reactive only in certain spaces.
For instance, my dog is a collie/cattledog mix I've had since she was a puppy. She grew up around other dogs and never had problems with them until she got attacked by a Shepherd mix because some idiot was letting his dog run loose because he was too lazy to hook her up to a leash to have her go to the bathroom even though there's a leash law and she was CLEARLY dog aggressive, standing up and charging from sighting mine from about 50ft away (i do not and will never blame a dog for bad behavior, I will blame the owner though). After that, she became reactive to shepherds/Shepherd mixes and would start to bark at them if any got within sight distance of her. I had to work with some larger non-reactive dogs to get her to be less reactive and more just leery but I still watch and i still try to get information about other dogs that might want to visit and play with her before agreeing to let her meet them. Yet I would classify her as dog friendly, because she is 99% of the time. It's just the one scenario with the one type of dog that makes her not.
She also is not a resource guarder-- EXCEPT if we are opening presents and another dog comes in to see what's going on. You see, Penelope loves to assist by gently tearing the wrapping paper off the present while you hold it. But if another dog comes up to inspect, she's snap and growl at them. This is a dog who sits pitifully while another dog shoves in and eats her food, or who comes to tell me she's sad because another dog took her favorite bone or toy, because she doesn't fight back. Heck, my parakeet used to fly down and land on her toys and this 70lb dog would just sit at look at her like "My touys..... :((((" and cry while Watson pecked and walked all over them.
Now take these stories and flip them. In a shelter, where there's a lot of noise and stress and smell, a dog may be resource guarding 99% of the time. A dog might be skittish and unable to be relaxed enough to not be reactive to other dogs or while on leash (unable to escape of their own free will). But you take them home and make the proper steps to introduce this dog to a new household? Maybe that changes. Maybe your established dog is just the right personality to not make the reactive dog react (dogs that do the "-sniff- .....neat. -ignores other dog-" behavior when encountering a new dog are great for practicing socialization with for more hyperactive/reactive dogs because they just Don't Care, for instance). Maybe the quiet and smell of your house unwinds the typically stressed out dog enough for them to be receptive to change. Maybe the new routine and increased attention helps shift that dog's personality and behaviors to the positive.
But what if it doesn't? THIS is why shelters and rescues warn you about behaviors they've seen. It's not to dissuade you from adopting, it's so you can look and say "OK it says he's not good with other dogs. I have a dog at home, maybe we can arrange a home visit to try them out?" Or "Oh it says he's not house trained. I have some time off work I can take, I should do that so I can work on getting him house trained and on a schedule when he first gets home with me.". It's so you dont just get a dog, turn it loose at your place and then potentially get this dog put on a list or, worse, euthanized if it bites your established dog or child or etc because you weren't informed. It's so that during the interview staff can ask you about your home and your previous experience with dogs and see if you'd be a good fit.
It's all for the good of the dog. They WANT someone to take them to their forever home and they would LOVE for notes like that to be proven wrong with the test of time and patience and love. What they're trying to avoid is that dog becoming just another statistic.