PETAs stance is that it's inhumane to forever house unwanted pets, which is why they prefer euthanasia over a life in captivity.
More on topic, my vegan, anti-fur wife is an active member of the Jane Goodall Institutes Jane's Peak Society and actually got the chance to talk to Jane at AK when it first opened, as Dr. Goodall took part in putting together the primate exhibits at AK together. While most animal lovers, my wife included, generally feel that living a life "on display" may not best the best situation for these animals, there is also the consideration to be made that in allowing the public to experience and appreciate these beautiful creatures up close and personal, a demand is built for keeping those animals who are still in the wild, and perhaps threatened, safe and unharmed. Couple that with the fact that the attractions throughout the park pour on the concept of conservation with a heavy hand (and rightly so) and you come up up with AK as our family's favorite destination within WDW.
In the end, it's all about where your friend's convictions lay, and what they feel is right and wrong. If she's of the more militant variety of animal lovers, who refuse to see the good found in something she might perceive is less than desirable, then I'd tend to agree with those here who suggest that it might be in your best interests not to try to talk your friend into doing what she isn't comfortable, even if it's for the sake of just enjoying your vacation together.