The propagation and rupture of mucus plugs in human lungs is investigated experimentally by injecting synthetic mucus in a pre-wetted capillary tube. The rheology of our test liquid is thoroughly characterized, and four samples of synthetic mucus are considered in order to reproduce elastoviscoplastic regimes of physiological interest for airway reopening. Our experiments demonstrate the significant impact of the viscoplasticity and viscoelasticity of mucus. In support to our experiments, we propose a one-dimensional reduced-order model that takes into account capillarity, and elastoviscoplasticity. Our model manages to capture the cross-section averaged dynamics of the liquid plug and is used to elucidate and interpret the experimental evidence. Relying on it, we show that the liquid film thickening due to non-Newtonian effects favors plug rupture, whereas the increase of the effective viscosity due to higher yield stresses hinders plug rupture. As a result of such two effects, increasing the polymeric concentration in the mucus phase leads to a net increase of the rupture time and traveling length. Hence, non-Newtonian effects hinder airway reopening.