Actually, massless particles must always travel at the speed of light, but they can still accelerate. Acceleration is speed plus direction. Thus if their speed can't change, their direction can still change, meaning they can still accelerate. Think of the massless photon bending around a star as it experiences gravitational lensing.
The more correct statement is that chargeless particles don't emit light without decaying and massless particles tend to be chargeless.