Depends on the animal. I know a decent zoo that has just simple waist-high walls around the porcupines and raccoon dogs for example.

They have space, but they can get pretty close. I guess a complete idiot with a cane could probably harass them, until someone stops them like “what the hell, asshole”. Or you know, until Everett True comes and causes permanent spine damage to them.

Obviously animals like bears, apes and big felines can’t get that close to people.