I've heard of too many rescue dogs being returned to rescue after seriously injuring, even killing, neighbourhood cats :(
Rescues have every right to be cautious, they don't want their rescue dogs causing injury, or killing, other pets/dogs in the home, they don't want members of the family nipped or bitten, they really don't want the dog returned to the rescue a few weeks down the line because the new adoptees decided it wasn't for them. Then they have an even more confused dog to deal with, now with an even longer list of behavioural challenges and likely even more restrictions needed.
Over the last month a local Husky has done a runner out of their garden with a 6ft fence, I've handed her over to the dog warden twice, other neighbours several more times. She's nearly caused accidents on the nearby busy roads. Security is important for dogs, some are very athletic and even a 6ft fence could be cleared/clambered over or bushes can be pushed through in pursuit of cats/squirrels etc.
Rescues have restrictions because they have to. They do their very best to match dogs with new owners, but that's not easy, especially when so many apply, potentially over 100 applications for popular dogs. Some will be arsey and entitled thinking "I've applied, now give me a dog". That's not how it works. Rescue workers are shouted and abused on a daily basis. And then they think they find a nice sane family, who return the dog a week later because they lied about their living arrangements just to get a dog :(