Like charges stabilize emulsions, whereas opposite charges break emulsions. This is the fundamental principle for many industrial and practical processes. Using micrometer-sized pH-sensitive polymeric hydrogel particles as emulsion stabilizers, we prepare emulsions that consist of oppositely charged droplets, which do not coalesce. We observe noncoalescence of oppositely charged droplets in bulk emulsification as well as in microfluidic devices, where oppositely charged droplets are forced to collide within channel junctions. The results demonstrate that electrostatic interactions between droplets do not determine their stability and reveal the unique pH-dependent properties of emulsions stabilized by soft microgel particles. The noncoalescence can be switched to coalescence by neutralizing the microgels, and the emulsion can be broken on demand. This unusual feature of the microgel-stabilized emulsions offers fascinating opportunities for future applications of these systems.