Why aren't bird/parrot owners held to the same standards as dog and cat owners?

Probably because birds are not as common pets as dogs and cats. Due to that, naturally there are a larger quantity of dogs and cats being neglected then birds.

All the time I hear about cases where people have hoarded dogs and cats for years.

I don't think that cats and dogs always get rescued before birds. I think it goes by a case by case basis. Those cats and dogs were seized quickly fortunately, but I'm sure many many cases are missed for years and years, or never discovered at all :-(

All animal owners are held to the same legal standards as far as I know.

ADDED: Tying a bird to a perch is very unhealthy. A bird's cage is basically the equivalent of a bedroom for the bird. Birds need personal space just like humans, a cage gives them somewhere to feel safe, and their own bit of territory. Being tied up is not kinder then being caged. Not to mention any responsible bird owner has a bird that is out of the cage much of the day anyway. My bird has free range of the house whenever I am home.

A bird that is tethered to a peach is trapped on that perch at all times. A bird in a large cage can climb\fly around its cage. It is very unhealthy and can lead to muscles atrophying for a bird to sit on the same perch all day long.

Well, that's not nice at all! Any considerate dog owner will pick up their dog's poops whenever possible. I am thinking that maybe your HOA can step in and do something about it if you present your case to them at the next HOA meeting. Since you have cameras installed, you have evidential proof of certain people not picking up after their dogs, which is against the law in many parts of the country. As a dog owner I can tell you that there have admittedly been a few "emergency" situations where for some reason or another I was stuck without a bag and I had no other way to pick it up, and I have always felt so tremendously guilty when that happens, but I assure you that I would never just leave my dog's poop on someone's private lawn. Psychologically speaking, though (since this is the Psychology section), do you think that some misanthropic neighbors purposely seek out your lawn as a poo target for the express reason of your signs and cameras? Sometimes, people are tempted to purposely defy signs by doing exactly the opposite of what the signs ask. This is especially true if you live in a neighborhood with a lot of kids and teenagers, or if you just have some annoying neighbor who thinks your signs are an eyesore and is trying to make a point, in a very childish way.

HELL YES! Of course bird owners should be held to the same standards. There's really not much more to say on the subject. There is absolutely no reason that people should think of bird abusers more highly than cat/dog abusers. In countries other than America, people often buy birds without cages. And they keep them from flying away by tethering them to a perch. >_>