The test itself is fine. But the interpretations based on Shoemaker's claims are unfounded. Basically he found high rates of certain HLA types in his mold patients, compared to world-wide rates of those types, and concluded that certain types result in susceptibility to mold, chronic lyme, and other things.
The problem is that HLA types are closely tied to ethnicity, and most of his patients would be western European, as well as patients of blended African and European ethnicity. Hence it is not valid to use worldwide rates of HLA types for comparison, since he was not looking at a sample of patients from a worldwide group.
This problem is easily illustrated by looking at the prevalence of the supposed susceptible HLA types in European-Americans in general. If we do the math based on his claims, around 85-90% of European Americans are in grave danger of reacting very poorly to mold, Lyme, or a couple other things. Which is a frankly ridiculous claim, in addition to being completely unfounded.
HLA data can be interesting or potentially useful for various things, but not for any reason related to Shoemaker's claims.