  The response of superconductors to controlled introduction of point-like
disorder is an important tool to probe their microscopic electronic collective
behavior. In the case of iron-based superconductors (IBS), magnetic
fluctuations presumably play an important role in inducing high temperature
superconductivity. In some cases, these two seemingly incompatible orders
coexist microscopically. Therefore, understanding how this unique coexistence
state is affected by disorder can provide important information about the
microscopic mechanisms involved. In one of the most studied pnictide family,
hole-doped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ (BaK122), this coexistence occurs over a
wide range of doping levels, 0.16~$\lesssim x \lesssim $~0.25. We used
relativistic 2.5 MeV electrons to induce vacancy-interstitial (Frenkel) pairs
that act as efficient point-like scattering centers. Upon increasing dose of
irradiation, the superconducting transition temperature $T_c$ decreases
dramatically. In the absence of nodes in the order parameter this provides a
strong support for a sign-changing $s_{\pm}$ pairing. Simultaneously, in the
normal state, there is a strong violation of the Matthiessen's rule and a
decrease (surprisingly, at the same rate as $T_c$) of the magnetic transition
temperature $T_{sm}$, which indicates the itinerant nature of the long-range
magnetic order. Comparison of the hole-doped BaK122 with electron-doped
Ba(Fe$_x$Co$_{1-x}$)$_2$As$_2$ (FeCo122) with similar $T_{sm}\sim$110~K,
$x=$0.02, reveals significant differences in the normal states, with no
apparent Matthiessen's rule violation above $T_{sm}$ on the electron-doped
side. We interpret these results in terms of the distinct impact of impurity
scattering on the competing itinerant antiferromagnetic and $s_{\pm}$
superconducting orders.
