I don’t have a lot of information on the species of cats that would get along with labradoodles, but I think that Persians might like them, especially a specific color, blue.  Some cats might not like them because they can be loud or mischievous.  I am not certain about the breed of cat that will not get along with the labradoodle.  I think that it would be good to try some things, like meeting the dog, and seeing how the cats act around them.  If the cats don’t like the dog, you can try giving them treats so that they associate the dog with treats.
assitant
I think a larger cat would be fine.  A Calico, American Shorthair, or Persian should be fine.
assistant
Do labradoodles get a long with cats?
user
Labradoodles are a cross between a Labrador Retriever and a Poodle.  In my experience, cats are often not fond of dogs, but some of them will get along with some dogs.  It is very difficult to predict which of your cats will get along with which dogs, especially because there are many different dog breeds and many different cat breeds.
assistant
What kind of cats get along with labradoodles?
user