Is it true that there are a Lot of cats and dogs wandering around the outside restaurants in Greece and the Greek islands while people are eating?
It depends on where, but yes. Cats mostly.
I wouldn't say there are a LOT of cats and dogs around restaurants in Greece, at least in the places I have visited (mainly Athens & and the islands). We have seen the occasional dog or cat wandering around, but not big groups of them. And there are plenty of restaurants with NO dogs or cats. There will be the occasional bird too. You are outside, after all. I would certainly not let this deter you from visiting this beautiful country.
There are lots of cats who live outdoors and people put food out for them. Cats also hang around restaurants, but the restaurant owners discourage them. Feeding a cat under your table can get you in trouble. There used to be quite a few dogs in Athens, but not really at restaurants. This is a different attitude than at restaurants in France and Italy where patrons often bring in their own dogs in a carry-bag.
Add Germany to what Laura said. And add much bigger dogs in all locations. I'm another animal lover and really enjoy seeing dogs and cats about.
Is the a reason for the question?