Dusty space plasmas contain negatively charged, heavy dust grains with characteristic frequencies much below those of usual plasmas. Pickup of ions of cometary origin by the solar wind is partly due to relative streaming between cometary and solar wind ions parallel to the interplanetary magnetic field, partly because of skewed velocity distributions perpendicular to it. Both pickup mechanisms excite low-frequency electromagnetic turbulence, which is altered by the presence of charged dust in cometary environments. We focus on parallel modes at frequencies below the cometary watergroup gyrofrequency. Existing firehose-like instabilities are stabilized at very long wavelengths. On the contrary, when modes would be stable in the absence of charged dust, the left-hand circularly polarized mode shows a new instability window. The scarce data available from recent cometary missions indicate that the wavelengths needed probably exceed the dimensions of the cometary structures. However, more data are needed to elucidate this.