PNIPAm microgels synthesized via free radical polymerization (FRP) are often considered as neutral colloids in aqueous media, although it is well known, since the pioneering works of Pelton and coworkers, that the vanishing electrophoretic mobility characterizing swollen microgels largely increases above the lower critical solution temperature (LCST) of PNIPAm, at which microgels partially collapse. The presence of an electric charge has been attributed to the ionic initiators that are employed when FRP is performed in water and that stay anchored to microgel particles. Combining dynamic light scattering (DLS), electrophoresis, transmission electron microscopy (TEM) and atomic force microscopy (AFM) experiments, we show that collapsed ionic PNIPAm microgels undergo large mobility reversal and reentrant condensation when they are co-suspended with oppositely charged polyelectrolytes (PE) or nanoparticles (NP), while their stability remains unaffected by PE or NP addition at lower temperatures, where microgels are swollen and their charge density is low. Our results highlight a somehow double-faced electrostatic behavior of PNIPAm microgels due to their tunable charge density: they behave as quasi-neutral colloids at temperature below LCST, while they strongly interact with oppositely charged species when they are in their collapsed state. The very similar phenomenology encountered when microgels are surrounded by polylysine chains and silica nanoparticles points to the general character of this twofold behavior of PNIPAm-based colloids in water.