Context. Understanding the chemistry of molecular clouds is pivotal to elucidate star formation and galaxy evolution. As one of the important molecular ions, HCNH+ plays an important role in this chemistry. Yet, its behavior and significance under extreme conditions, such as in the central molecular zones (CMZs) of external galaxies, are still largely unexplored. Aims. We aim to reveal the physical and chemical properties of the CMZ in the starburst galaxy NGC 253 with multiple HCNH+ transitions to shed light on the molecule's behavior under the extreme physical conditions of a starburst. Methods. We employed molecular line data including results for four rotational transitions of HCNH+ from the ALMA Comprehensive High-resolution Extragalactic Molecular Inventory (ALCHEMI) large program to investigate underlying physical and chemical processes. Results. Despite weak intensities, HCNH+ emission is widespread throughout NGC 253's CMZ, which suggests that this molecular ion can effectively trace large-scale structures within molecular clouds. Using the quantum mechanical coupled states' approximation, we computed rate coefficients for collisions of HCNH+ with para-H-2 and ortho-H(2 )at kinetic temperatures up to 500 K. Using these coefficients in a non-local-thermodynamic-equilibrium (non-LTE) modeling framework and employing a Monte Carlo Markov chain analysis, we find that HCNH+ emission originates from regions with H-2 number densities of similar to 102.80-10(3.55) cm(-3), establishing HCNH+ as a tracer of low-density environments. Our analysis reveals that most of the HCNH+ abundances in the CMZ of NGC 253 are higher than all values reported in the Milky Way. We perform static, photodissociation region, and shock modeling, and found that recurrent shocks could potentially account for the elevated HCNH+ abundances observed in this CMZ. Conclusions. We propose that the unexpectedly high HCNH+ abundances may result from chemical enhancement, primarily driven by the elevated gas temperatures and cosmic ray ionization rates of shocked, low-density gas in the nuclear starburst regions of NGC 253.