My relationship with a guy just ended over something else (he really wants kids) but if it hadn't, there's a good chance I would have ended things with him because of his dog. I really love dogs, but I don't like inconsiderate dog owners, and I don't like being around their poorly behaved dogs. His dog was so terribly behaved, and it was all the human's fault. I was embarrassed to be out with him and his dog.
Plus, he let his dogs pee all over his house and destroy the furniture, so it was smelly and disgusting to be in there.
If there is a leash law, leash your dog. I have been attacked by at least 3 dogs while out running, and one of my acquaintances was severely mauled (now wheelchair bound) by three dogs while she was out running. Pay attention to your surroundings so that you don't create a trip wire for a bicyclist because your dog is on a flexi leash across the bike path. If a park says no dogs, just go someplace dogs are welcome.
Inconsiderate people are everywhere (I will save my rant for inconsiderate cyclists, and I bike everywhere) and it really makes me upset when they do this with dogs because I had started to develop a phobia of dogs after being attacked so often.
So anyway, rant out of the way and back to dating/dogs.
I declined a second date with a guy who was way too into his dog. We went to the art museum and at every painting, he told me what his dog would think about it.
"I could never have that painting in my house. The purple would give Lizzie nightmares!"
"Lizzie would be so calmed if I could have this painting for her to see right before she went to bed" etc. etc. etc.
At the end of the date, I got a bit snarky and asked how Lizzie could possibly tolerate him spending a couple of hours on a date with me. He responded that he'd played fetch with her for a couple of hours prior, he promised not to be gone too long, and would take her to the dog park when he got back.
YIKES!!! Not touching that with a 10-foot pole!
That being said, I have parrots, and I have fully expected them to be something that guys wouldn't want to deal with, but all of the guys I've dated long enough to know about/meet them love them and think it's a funny (as opposed to creepy) quirk. Haven't been in a long-term relationship with anyone, so maybe they would change their minds when they were around them more often.