During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. In this talk, I will present a two-layer multiplex network for the coupled spread of a disease and conflicting opinions. We model each process as a contagion. On one layer, we consider the concurrent evolution of two opinions — pro-physical-distancing and anti-physical-distancing — that compete with each other. The disease evolves on the other layer, and individuals are less likely (respectively, more likely) to become infected when they adopt the pro-physical-distancing (respectively, anti-physical-distancing) opinion. I will present approximations of mean-field type by generalizing monolayer pair approximations to multilayer networks; these approximations agree well with Monte Carlo simulations for a broad range of parameters and several network structures. Finally, I will present numerical simulations that illustrate the influence of opinion dynamics on the spread of the disease from complex interactions both between the two conflicting opinions and between the opinions and the disease.