All other variables being equal, how does waveform complexity of a plane wave affect shielding effectiveness? Is it easier to attenuate a sine wave or a complex waveform?
In almost all cases, where linearity holds, it makes no difference.
You can analyse a complex waveform into a superposition of component sinewaves. An attenuator will reduce each, possibly by a different amount.
If the attenuator shifts the phases of the components, this may shift where the peak occurs, and so the ratio of peaks of output to input may be slightly different to the ratio of powers.
If your fields are so large the attenuator goes non-linear, then the complex waveform will likely send it non-linear at a lower power, as its peak to RMS ratio will be higher than that of a sinewave. Whether that means it attenuates more or less will depend on the detail of the non-linearity.