Dusty plasmas contain charged dust grains which are much more massive than protons, carry high negative charges due to preferential capture of electrons, and do not have a fixed charge. Fluctuations in the grain charges due to liberation or capture of additional electrons and protons translate as mass and momentum losses or gains for the electrons and ions, which can render linear modes unstable. For low-frequency modes with quasi-immobile dust grains we derive a whistler-like wave, and discuss its stability. If also streaming effects are taken into account, the modes can be stabilized for specific values of the different parameters controlling the momentum transfer and the streaming. This might be relevant for different kinds of astrophysical and heliospheric plasmas.