As I understand it, ambient speakers don't do anything for the animals and are just there for sound effects for guests.
The only thing that seems to help is to have one way glass and to make sure food, water, enrichments etc. are available well back from the barriers in hidden parts of the enclosure. I haven't seen a clear pattern with the do not disturb signs. They may help a bit. I've found the animal stress to be a major issue in timed scenarios and some of the career scenarios, where you are usually pinched for money and staff, and they never seem to have one-way barriers enabled unless you pull one of your mechanics out of maintenance duties to research it (and it takes forever for them to do this too).
I was trying to do the Oregon zoo one the other day, and I decided I really do hate having springbok. They are very precious, delicate little snowflakes that are obviously not suited for captivity
It does limit one's ability to experiment with different designs and aesthetics for certain habitats, and guests then get annoyed because they can't see the animals well. I've had to move shy, and even neutral, animals out of habitats with elevated viewing areas, for instance, and out of habitats with cute fences set up with null barriers once guest numbers get to a certain level. Until there's the option to limit guest numbers in certain areas of the zoo, it limits how you can set up habitats.
As an aside, it seems the protesters add to the animals' stress with their shouting and waving signs around.
I don't know how the protesters can show up so fast, or how they have any clue that animals are stressed the second I get the notice. But it's also not clear why they would ever stop protesting, since most of these folks (in real life) are against zoos in general, and once they decide one is "bad" they aren't likely to quit. So gratitude for small favors.