White fluffy is completely different than your small bulldog. And outdoors is different than what happens in the house.
We have a mini Aussie. He is about 10 pounds and very fluffy. In the house all my dogs are small dog safe and cat safe. We also have a 3 pound chi mix and a 12 pound cat.
However, outside my greyhounds have chased and even grabbed the mini Aussie. They don't even mess with the chi but the hairy dog bounces and the hair shakes and, well, looks like a stuffed toy rolling through the yard.
You don't need to muzzle your dog but you do need to take some precautions. Any new dog, fluffy or not, should have some precautions when meeting.
We shaved the dog. . Stopped all the problems.