The Sohma family wasn't normal. How could it be with many of its members cursed?
Even the members who weren't cursed might as well be. They lived with the secret. They had to wonder why their relatives weren't normal before they were told.
Even with the animosity between different members of the family, they all had a strange, but permanent bond. The curse bound the family together. It bound anyone else that happened to find the secret out to the family indefinitely.
But was the curse a normal family bound?
The curse changed lives. But most predominately, it bound lives.