  The antiferromagnetic layered compound EuCd$_2$As$_2$ is widely considered as
a leading candidate of ideal Weyl semimetal, featuring a single pair of Weyl
nodes in its field-induced ferromagnetic (FM) state. Nevertheless, this view
has recently been challenged by an optical spectroscopy study, which suggests
that it is a magnetic semiconductor. In this study, we have successfully
synthesized highly insulating EuCd$_2$As$_2$ crystals with carrier density
reaching as low as $2\times 10^{15}$ $\text{cm}^{-3}$. The magneto-transport
measurements revealed a progressive decrease of the anomalous Hall conductivity
(AHC) by several orders of magnitude as the carrier density decreases. This
behavior contradicts with what is expected from the intrinsic AHC generated by
the Weyl points, which is independent of carrier density as the Fermi level
approaches the charge neutrality point. In contrast, the scaling relationship
between AHC and longitudinal conductivity aligns with the characteristics of
variable range hopping insulators. Our results suggest that EuCd$_2$As$_2$ is a
magnetic semiconductor rather than a topological Weyl semimetal.
