Note the title is "Keep your identity small", not "Reduce your identity to zero". While I
think I can see what you're getting at, I'm not sure I follow the logic. Bear with me for a moment: In the case of slavery, I wouldn't want someone to consider themselves a slave, I'd want them to consider themselves a human being and expect to be treated as such. Similarly for anyone dealing with harassment or unjust marriage laws. These conditions aren't unjust because one is a slave or a woman or gay. They're unjust because you're a human, and the conditions are inhumane. A slave doesn't want to continue to be a slave; a woman doesn't want to have to put up with harassment because they're a woman; a gay man doesn't want to be treated differently because he's a gay man: they want to be treated fairly and justly because they're human.
I think one of the things Graham is pointing towards is finding what is common among people, rather than focussing on the differences. A couple of sentences that stood out to me when I read it were "More generally, you can have a fruitful discussion about a topic only if it doesn't engage the identities of any of the participants. What makes politics and religion such minefields is that they engage so many people's identities." I read that as focussing on those topics in common.
None of this is guaranteed, of course. But I think it's a more constructive way forward than focussing on what divides people.
Would you expand on what aspects of the piece you took to supporting the conclusions and examples you provided above?