Actually, cat purring is my favorite noise on my white noise app! My ears love it.
Animals certainly can be sensitive to noise and also experience anxiety, as we do. My dog has separation anxiety and when I was reading a professional article about it recently, was interested to see how similar the neurological mechanism was to anxiety in humans. I am not sure if animals' brains/neurological systems would compensate for inner ear hair cell death by generating tinnitus. Dogs and cats certainly can go deaf, or be born deaf.
Regardless, your pets, just like you, should not be subjected to loud noises.