If the audience is considered as a group of people
This is true, but audience is still a singular noun. Because it refers to a single group, not multiple groups.
The audiences listen to the bagpipes
There's where you'd use the plural noun form.
People means "multiple persons" (plural of person)
The people listen to the bagpipes
Then it has to be changed into tag question. The answer key said: "The audience listens to the bagpipes, don't they?"
It is an impersonal pronoun and can't be used to refer to people. This is a strongly observed convention in English.
Another situation where you really need a pronoun--but English is unhelpful--is if you don't know whether to choose between him or her - they/their/them has a tendency to be used. This is the "singular they" and the Wikipedia article shows examples of its use from the 1300's.
A potential employee would need to have passed their drug test to get hired (do not know whether employee is male or female).
"The audience listens to the bagpipes, doesn't it?" is not wrong, but since an audience is comprised of people, the temptation to do a similar thing to the "singular they" is strong.
It avoids any allusion that it might refer to the nearest non-human object, which are the bagpipes, to someone who isn't listening closely. Someone might even think doesn't it refers to something earlier in the conversation they may have missed.