Why are there dogs such as Golden Retriever, Labrador or Corgi allowed in HDB flats? Is there an exception given to such dog breeds?

I dont think they are allowed. The rule is not strongly enforced unless there are complaints.

Of coz not

Golden retriever is gentle dog, if they are not giving you any hassle, just leave this alone?

It will never work unless serious thing happen. For eg. Walk the dog you are required to put on leash and mouth guard for the dog. How many of them did it? So just suck it up. They cannot even resolved noise issue between neighbour. So what make you think they can resolve this.