No experience of CP, but our cat always comes on holiday with us, and very happily. Some cats are more bonded to their people than the home itself, and so as long as they are with their people and their other needs are met, they are happy.
We have what we need to take and what we need to do down to a fine art now, and we have a routine our cat knows and is happy with. Extreme care has to be taken with doors and windows, but that is only as at home if you have an indoor cat. I do know people who take their cats out and in the garden when on holiday, but that's not a risk I would take.
Our cat has never caused any damage or mess. Some cats would, just like some dogs would, in which case neither should be taken to holiday accommodation or, at the very least, never left unsupervised.
And that is one issue you do have to address when holidaying with cats, because most accommodation owners state that pets should not be left unsupervised, so you have to take them with you whenever you go out for the day or evening. That's not usually a problem with dogs - and that's who they are talking about 99% of the time when they say 'pets' - but most people can't take cats and other pets like parrots and guinea pigs out with them. We take an extra-large crate with us for this reason. It's big enough for a bed, covered litter tray and bowls with food and water. Whenever we go out or go to bed, our cat goes in the crate. This works well and is accepted by holiday accommodation owners in our experience. It only works though because our cat is happy with it, already associating time spent in the crate with food, sleep, familiarity and security. We also take our cat's well-used scratching post, some toys and a throw for the sofa.
So far, we have only come across two holiday accommodation owners who only accept dogs and not any other pets. One is the National Trust - such a shame, as we'd love to stay in several of their properties - and another owner who said she didn't like cats and her husband was allergic. I always check that a cat is acceptable to owners if it's not stated as 'all pets accepted, not just dogs' in the advert, because it's only fair to the owner. I also don't want to be in breach of the rental contract, and I want to be relaxed during the holiday about having our cat there, not concerned I'm doing something wrong and might get found out.
I'd go as far as to say that our cat actually enjoys coming on holiday, especially having some interesting new views and wildlife to watch from the windows and new fires to curl up by. Feedback from owners has always been really positive, including that our cat isn't bringing mud in like dogs and there's never any dog mess left in the garden to clear up. We've always been welcome back, anyway.
I have more tips about travelling and holidaying with cats if anyone needs them.