I think that's a little too simplistic. Visitors would have to, if you already put up such a sign, also about why PETA is such a problem for all pet owners. I always think it's better for zoos to show their important role in species conservation than to say, "Don't support PETA and Co!"
@Animal I imagine employees would be happy to talk to guests if they'd like to know more. Peta likes to pretend they care about conservation and pet ownership, so talking about those things doesn't really get across an anti-peta message.
The problem here is how guests could receive this message. Maybe they thought that PETA does good for animals. Now they read that PETA is against zoos and more importantly: This zoo. The thought can be "If the well respected PETA is against this zoo, maybe I should be too!"
Framing is an important instrument and all sings and education should be second guessed all the time. It is easy to have a message that gets across the complete wrong way.
Also should a sign speak for itself and not be in need of staff to explain how and what they mean by the words on it.
Never the less, I know about PETA and other organisations like them and view them as such. But most normal zoovisitors might not and a sign like this might just be counterproductive.