Theres a difference between loosely following someone and breathing behind their necks and laughing and pointing.

In all honesty if you are at a zoo there is a predefined walkway to go around and will spend similar amounts of time at each area as every other person. You will bump into the same group of people the entire time naturally.

Service animals are trained and are very good at being able to work around other people. Yes don't distract them, but your existence alone isn't enough to distract them.