The article is particularly concerned with personalized/precision medicine: tailoring therapy to specific individuals based on their genetic background.
The article is in particular talking not about stem cell lines, but about cell lines derived from patients with cancer. These cell lines are studied to understand what made those cells cancerous, to both understand mechanisms of cancer and develop treatment.
How are cells different depending on the ethnic origin?
The issue raised is not a specific difference, but rather the unknown. If you only study variation among European-derived cell lines, you cannot possibly understand human-wide variation. Further, if you have just one cell line labeled as "African-American" and use studies with this cell line to make decisions about how you're going to treat all Americans with Black/African ancestry, and that one cell line is also mostly of European origin, you shouldn't expect that research to result in good outcomes for African-American/Black patients.
An example of how this might work is that a bunch of study into cancer cell lines identifies some specific mutation associated with cancer, and some pharmaceutical treatment that is highly effective in cancers based on that mutation (perhaps an antibody-based treatment). The next step would be to identify patients who carry that specific mutation or where that mutation is present in biopsied tissue, to give them that customized therapy. However, if all the cell lines you study come from people with European ancestry, only people with European ancestry are likely to have any of those specific mutations, and everyone else is left out.
In particular, African populations are more genetically diverse than populations anywhere else, presumably because humans first evolved in Africa and subsequently traveled elsewhere. Therefore, studying mostly people of European ancestry merely because they are the dominant group in a specific high-wealth country like the US is leaving the majority of human genetic diversity out of study.
The article you linked about prostate cancer seems like a good place to further understand this: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7219314/
It describes how therapies developed because they are effective in a single prostate cancer line didn't actually work for most people with prostate cancer, and that subsequent efforts to study therapies in multiple cell lines have not benefitted "Men of African Ancestry" because those cell lines are predominantly derived from "Men of European Ancestry".