One doesn't stand in for the other, privilege isn't even fixed. In some circumstances even white males are unprivileged. There is nuance, and 'ethic minorities' completely misses the nuance.
Also is colonisation the problem? The Chinese went to America of their own will, do they have less moral standing than black Africans? And then we get to native North Americans. At what point did they stop having the privilege Vis a vis the founding fathers? Are the founding fathers morally wrong to have gone to North America or just morally wrong to forcefully move the natives from their lands? Further I'm not Catholic so I don't buy into the white guilt thing based on what some other white people did centuries before, I'm more interested in the here an now.
So as I said before. If you want to make a case for why certain groups need protections, why certain groups need positive discrimination to reach parity I'm open to that. But pointing back 700 years and saying ethnic minority isn't an argument.