This is the point - this is about classes not individuals.
Oppression, discrimination, etc is about classs, not individuals, although oppression is obviously perpetrated and experienced by individuals. But the reasons behind it are class reasons, not because of the qualities of individuals. It's ALL black people, or ALL Jews, etc.
I get the offence. As a white person, if I lived in some southern US states, I am sure I would detest the way that many white people talked about black people behind closed doors and that I would do my utmost to distance myself from that. Whilst on an individual level, I may not be an oppressor (although I may need to examine the ways in which I behave), I would still be a member of the class of people that oppress the class of black people on racial grounds.
Being hurt by being included in that class is unfortunate, but I am still a member of that class. My issues concerning not wanting to be one of 'those white people' are wholly separate from the issues black people experience at the hands of 'those white people'.
My individual feelings as a white person who objects to racism are important. Certainly to me. And probably shared by other white people who object to and reject that socially constructed and socially acceptable aspect of whiteness. But when it comes to respecting that e.g. some Black Lives Matter protests need to be a unified BLACK voice and BLACK presence, that funding etc earmarked for black people is because of class based oppression, with me as part of the oppressor class and them as part of the oppressed class, I think I actually need to suck it up and butt out.
I would hate for class-based analysis to get in the way of personal friendships and relating on an individual level. But this is not what this is about. It's not personal. It can't be personal.