I have heard stories of people getting bitten and cats not leaving visitors alone, often going in and around restaurants. I am not a cat person AT ALL and I am actually allergic to them. I have never been to Greece but will be going in 2023. I will be staying either in Athens or Crete, I am not sure yet - it will be a family trip. Do I need to worry?
You are going to run into cats and many of them will approach you because people commonly feed them. The only advice I can give you when going is to avoid strolling around at dusk and dawn. This is when the cats are most active. Also do not go to restaurants that offer outdoor seating as these do attract the felines. November, December, and January are the best months to avoid the cat heat season when most female cats will be looking to mate and cats in general will be more active.