Ideally you answer these questions honestly, but most places will be very wary of someone that openly supports any animal rights organizations in an interview or application scenario. Keep in mind that as a vet student you will be working with animals kept for production purposes and will likely have teaching animals for certain labs (not to mention using technology and medications made possible by animal use in research).
That being said, there are definitely ways to convey that you feel passionate about animal welfare that are not as alienating as aligning with an animal rights organization.