Abstract Epsilon-near-zero (ENZ) materials have recently emerged as a promising platform for infrared nanophotonics. A significant challenge in the design of ENZ-based optics is to control the dispersion of ENZ modes that otherwise have a flat profile near the ENZ frequency. Strong coupling with an optical cavity is a promising approach to ENZ dispersion engineering, which however has limitations due to the lack of tunability or nanofabrication demands of the cavity employed. Here, we theoretically and numerically show that much of the limitations of previous approaches can be overcome by strongly coupling the ENZ mode to an unpatterned Fabry–Perot cavity. We demonstrate this unprecedented ENZ dispersion control in coupled cavities by designing tunable infrared polarizers that can absorb s and reflect p-polarized components, or vice versa, for almost any oblique angle of incidence, i.e. omnidirectional polarizers. The feasibility of active control is also demonstrated using a phase change material within the cavity, which predicts dynamic switchability of polariton dispersions across multiple resonant levels at mid-infrared wavelengths. These results are expected to advance the current understanding of strongly coupled ENZ interactions and demonstrate their potential in tailoring dispersions for active and passive control of light.