Diane Abbott is undeniably the authority on receiving racist, sexist, and myriad other forms of abuse. She has experienced it from the days of the green inked letter, and given many accounts of how such abuse, whilst heightened these days, isn't something new. There was a study done that showed around half of all abusive tweets to female MPs were directed towards Diane Abbott alone.
Clearly the narrative that's pushed by these abusive tweets is nonsense - she wasn't making constant gaffes during her long tenure on This Week. However, she is not by any means perfect, and she is on record making comments and saying things that are racist and offensive.
In the end, the latter could never excuse the former, and should she ever get into government she will be able to set the record straight. After all, who would doubt her convictions of being anti-racist and anti-sexist?