  Breaking Hermiticity in topological systems gives rise to intriguing
phenomena, such as the exceptional topology and the non-Hermitian skin effect.
In this work, we study a non-Hermitian topological crystalline insulator
sitting on the Kekul\'{e}-modulated honeycomb lattice with balanced gain and
loss. We find that the gaplessness of the topological edge states in the
non-Hermitian system is insensitive to edge geometries under moderate strength
of gain and loss, unlike the cases of Hermitian topological crystalline
insulators that depend on edge geometries crucially. We focus on two types of
gain and loss configurations, which are $PT$-symmetric and $PT$-asymmetric,
respectively. For the $PT$-symmetric configuration, the Dirac point of the
topological edge states in the Hermitian molecular-zigzag-terminated ribbons
splits into a pair of exceptional points. The edge gap in the Hermitian
armchair-terminated ribbons vanishes and a Dirac point forms as far as moderate
gain and loss is induced. The band gaps of edge and bulk states in the
Hermitian armchair-terminated ribbons close simultaneously for the
$PT$-asymmetric configuration.
