  We examine type D ASEP, a two--species interacting particle system which
generalizes the usual asymmetric simple exclusion process. For certain cases of
type D ASEP, the process does not give priority for one species over another,
even though there is nontrivial interaction between the two species. For those
specific cases, we prove that the type D ASEP is self--dual with respect to an
independent product of $q$--Krawtchouk polynomials. The type D ASEP was
originally constructed in arXiv:2011.13473, using the type D quantum groups
$\mathcal{U}_q(\mathfrak{so}_6)$ and $\mathcal{U}_q(\mathfrak{so}_8)$. That
paper claimed that certain states needed to be "discarded'' in order to ensure
non--negativity. Here, we also provide a more efficient argument for the same
claim.
