a mark of shame or discredit
stigma - shame
If there's a ‘stigma’ around something, then there is a negative stereotype, reputation, or association attached to it. It is generally as a result of a societal norm or wide perception that a particular situation or even illness is something to be ashamed of, even if that is entirely unfair. People often fight to overcome stigmas.
Charities and campaigners have worked tirelessly to remove the stigma surrounding the issue of mental health.
Being divorced or a single parent no longer carries with it the social stigma that it once did.
An open and fair society should never stigmatize one group of people. It only leads to inequality and conflict.