No, it works with everyone if the people building and training the system know what they are doing.
It's well known that if you train the system with a widely unbalanced distribution of ethnicities, it won't work well for ethnicities that appear rarely in the training set.
This has absolutely nothing to do with *which* ethnicities are rare. It's just a direct consequence of how learning works (in machines *and* in humans).
The fix is totally trivial: if you want comparable levels of performance on samples of various subcategories, just make sure your training set contains similar proportions of samples from each subcategory.
The issue is that in the early days of deep learning-based face recognition, a number of facerec service providers (e.g. AWS, IBM, etc) didn't pay attention to this. Their systems worked ok for widely-represented ethnicities in their training set, but not for others. Some folks mistakenly jumped to the conclusion that facerec is unavoidably discriminatory.
It's not.
You just have to do it right.