I understand the quote as meaning that we should speak out even when groups we do not identify with are being oppressed.
But you seem to understand the quote as meaning that we should identify with as many groups as possible.
I very much doubt the author of the quote meant it the way you do, and even if they did it just sounds very wrong. It's expected and accepted to not care about any other group than the ones you identify with then? I do not identify as LGBT or as a woman, so I should not speak out for LGBT and women's rights? What about groups that will remain small because you can't just decide one day to identify with them, they're screwed?
Even if you are not a jew, why couldn't you have a discussion about jews? In fact, isn't that Paul Graham's entire point, that if it's not part of your identity (i.e. you're not a jew), you can have a much more reasonable conversation about it?
The point is not that this person should have expanded his identity till he was a Socialist. The point is that there are principles that you should stand up for in the defense of people outside your identity group.
A socialist, a trade unionist, and a Jew are still all people. You should be a human being, and treat others as such. If your identity is, as per your example, "right-wing", "German", "Christian", "pagan", "working class", or "member of the NSDAP", then you may not feel that your shared humanity is more important than your other identities.
I don't know which reading is correct, but I prefer mine.
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First they came for the Socialists, and I did not speak out — Because I was not a Socialist.
Then they came for the Trade Unionists, and I did not speak out — Because I was not a Trade Unionist.
Then they came for the Jews, and I did not speak out— Because I was not a Jew.
Then they came for me — and there was no one left to speak for me.
TLDR: paul graham is sofa philosopher.