Maybe I'm playing the devil's advocate here but I wanted to point something else out though, and it's as a long-time dog, cat and moluccan cockatoo (<sigh>) owner.
Not everyone loves animals, not every space has to allow them - or at least not leash-free. There is a park near my house with several "No Dogs Allowed" signs outside which is usually crawling with owners playing catch with their pets, not to mention a second one clearly marked as leash-only which similarly sports several furry critters running around.
This isn't good. People who don't appreciate, are afraid of (or, yes, allergic to) animals there should be some public places they can visit without being triggered. Similarly I'm quite aware one of my dogs isn't very well behaved in the presence of other small dogs, and as such it's stressful when I walk her in the leash-only park and she's approached by free-roamers as that's a fight waiting to happen.
We need to be mindful of other people too.