This is a racial comment. It was a common belief at that time that the Africans were immoral and unfaithful. Black fabric means that the fabric has become weak , in this context it means false due to the chemicals used to make the black dye. How people are judged and people form opinions against them because of the color of their skin? Is is even morally correct to form such prejudices?
But were they false As o’erdyed blacks,
Act 1 Scene 2