The flow of granular materials through narrow openings governs flow and process efficiency in a variety of industrial settings. As the use of soft particles and other soft micro-materials becomes more widespread in consumer products, we seek to understand characteristics of granular flows beyond powder flows. We study clogging through a 2D hopper in systems consisting of a combination of soft and rigid particles of different sizes and mixing fractions. Our experimental results show that soft particles play a lubricating role in the flow of rigid spheres due to their deformability and slick surface, but the size of rigid particles influences clogging more than the size of soft ones. We simulate our results using a modification of the Durian bubble model to accommodate mixtures of particles of different softness. Without any adjustable parameters, the simulation results capture the clogging probability of soft-rigid particle mixtures through a 2D hopper.