Different cultures work in different ways (or they wouldn't be different cultures) but the culture someone chooses to follow/adopt is a personal choice, entirely within their own power - not governed by the colour of their skin.
Dianne Abbotts tweet, on its own is literally 'taken out of context'.
The context was a discussion on how black community communities and black leaders are presented in the media and to politicians - asking what a 'black community' is actually supposed to be, and so who/what those 'leaders' are supposed to be representing.
In this discussion Abbott rebuked the other participant for asking if the the term 'black' on its own was meaningful. Abbott suggested that was a valid line of discussion but that it should be kept quiet/private (don't wash dirty linen in public) and was a line of discussion that 'white people' like using to oppress others.
So 'in context' the tweet is (if anything) more racist than when taken out of context.
Its impossible to 'know' what someone else really believes - but if Abbott is judged by her words, she is undoubtedly a racist.
Equality Campaigner?I think applying this title to Abbott is disingenuous - as her purpose does not seem to be 'equality'.
Her purpose is the advancement of those she considers to be 'black people', whether this makes them equal to others or not doesn't seem to matter one way or the other, as long as they advance others can 'go hang'.
And if you happen to have a black skin, but don't consider yourself primarily a 'black person' then you really better watch out for her ire.
The Real Damage her Racism DoesIn the past the KKK and the Nation of Islam cooperated on the basis that they both supported a division of the races - the heavy-weight boxer Muhammad Ali addressed a KKK meeting.
Abbotts racism, drawing a line between 'black people' and 'white people', is no different.
In todays Sunday Times Rob Liddle (a humorous columnist, so with some comedic licence) quoted an earlier Dianne Abbot quote where she suggested that black mothers worked harder for their children than white mothers - Liddle suggesting they have to 'because the black fathers are nowhere to be seen'.
As a joke about a stereotype it may be amusing, but if taken at all seriously is offensive towards the millions of black fathers do take responsiblity for their families. Abbott's comments as a politician is what maintains this kind of humour.
Abbotts racism gives licence to all racism - the colour of her skin should make no difference to how she is judged.