But I (a black African man) can never truly know or experience what the average Uyghur goes though day to day, because I just haven’t lived it.
So no, when we say that, we are not “excluding” anyone - in fact the more allies a minority has, the more likely they will achieve equality. But lived experience is different.
However lived experience can also introduces biases — for instance, would you trust a court of law to deliver justice if the victim was also judge and jury? That lived experience which provides sensitivity and also can make one too close to the matter at hand to see things clearly.
I think people with and without lived experiences can pull together and make positive contributions.
I say this because there are so many examples of solutions proposed by people with lived experience that are utterly counterproductive, because they shut out the voices of those without lived experience but who might have balancing views drawn from the broader human experience.
So yes you’re right anyone can empathize. But I don’t think that’s what OP is saying. You really cannot fully understand unless you live it. Just like you cannot understand true poverty in African countries, when you’ve spent your whole life living in a (relatively) rich one.