I recently came across a report that attempts to quantify the total economic contribution of Hispanics to the broader US economy, in what the report calls the Latino GDP. It suggests that Hispanics as a group had a GDP of $2.6 trillion based on 2018 economic data, and that if Hispanics living in the US were an individual nation, it would be the eighth largest economy in the world, as measured by GDP. Is it possible and appropriate to use GDP to measure the economic contributions and relative wealth of a distinct racial and/or ethnic group that lives within the United States? Would not factors such as general industry infrastructure investments, shared national resources, federal government spending, etc. impact ALL individuals within the US as part of the US national GDP and thus blend - if not blur - any attempt to create a racial/ethnic GDP figure?
I am not familiar with the report you mention, but conceptually it is possible to construct and measure GDP by specific demographic groups, say by educational levels, race/ethnicity, gender, or age. The precision of those indicators would depend on the type of data available, and the soundness of the imputations needed. There are well-known difficulties in estimating aggregate GDP, but also well-known adjustments. For example, GDP includes imputed rental values of owner-occupied homes.
For concreteness, suppose there are two groups, A and B, producing two final goods, apples and oranges. There are three ways to determine the contribution of each group to the total value of production: the production approach, the income approach, and the expenditure approach. The production approach would require information about how many apples and oranges each group produces. Full data on this is likely unavailable, or even unfeasible, but if most of group A produces apples and most of group B produces oranges, then some bounds can be obtained for the contribution of each group.
The second approach, the income approach, seems more promising for this purpose. This approach requires knowing how much each group receives from participating in the production process. Information on factor payments by a group may be more widely available but still likely incomplete.
Finally, the expenditure approach would require information about how each group spends its income, who bought the apples, and who bought the oranges. In practice, all three approaches are utilized when estimating aggregate GDP. The three methodologies could also be combined when estimating group-specific GDPs. Any estimate would have noise, some more than others, but they are likely to be informative.
You wonder about the impact of shared (public) resources on these calculations. I would think that, in principle, the calculations will still be fine. More public resources, like infrastructure, enhance production, income, and expenditures in ways that could impact different groups differently. Tracking those three outcomes (production, income, and expenditures) could tell us how much the public source benefits every single group.