  The non-interacting and non-Hermitian, parity-time ($\mathcal{PT}$)-symmetric
Anderson model exhibits an exceptional point (EP) at a non-Hermitian coupling
$g=1$, which remains unrenormalized in the presence of interactions (Lourenco
et al, arXiv:1806.03116), where the EP was shown to coincide with the quantum
critical point (QCP) for Kondo destruction. In this work, we consider a quantum
dot hybridizing with metallic leads having Rashba spin-orbit coupling
($\lambda$). We show that for a non-Hermitian hybridization, $\lambda$ can
renormalize the exceptional point even in the non-interacting case, stabilizing
$\mathcal{PT}$-symmetry beyond $g=1$. Through exact diagonalization of a
zero-bandwidth, three-site model, we show that the quantum critical point and
the exceptional point bifurcate, with the critical point for Kondo destruction
at $g_c=1$, and the exceptional coupling being $g_{\scriptscriptstyle{EP}} > 1$
for all $U\neq 0$ and $\lambda\geq 0; \lambda\neq U/2$. On the line
$\lambda=U/2$, the critical point and the EP again coincide at
$g_c=g_{\scriptscriptstyle{EP}}=1$. The full model with finite bandwidth leads
is investigated through the slave-boson approach, using which we show that, in
the strong coupling regime, $\lambda$ and interactions co-operate in strongly
reducing the critical point associated with Kondo destruction, below the
$\lambda=0$ value.
