  Exceptional points with coalescence of eigenvalues and eigenvectors are
spectral singularities in the parameter space, achieving which often needs
fine-tuning of parameters in quantum systems. We predict a persistent
realization of nodal magnon-photon polariton, i.e., a polariton without any gap
splitting in a thin ferromagnetic insulator film sandwiched by two normal
metals, which persistently exists when the ferromagnet is sufficiently thick
$\sim 100$~nm. We perform the model calculation beyond the perturbation theory
using a classical approach, develop a quantum scheme able to account for the
Ohmic dissipation, and find ultrastrong coupling with coupling strength
comparable to the bare magnon frequency. Via revealing a simple conversion
relation we extend this formalism to superconductors and predict the gap opened
by the ultrastrong coupling strongly depends on the direction of polariton
propagation. Our findings may help search for robust non-Hermitian topological
phases in magnonic and spintronic devices.
