Diffraction does not result in coloured light.
It has a much bigger impact and can change the nature of light from being a wave to being a particle.
The mother of pearl explanation has more a point but judging on pictures to me it does not look like the wishy-washy effect of mother of pearl.
On your picture each segment of light (wavelength) is clearly differentiated and in the order of appearance like the typical rainbow.
This effect is called interference where light is passing partly through and is partly reflected.
The overlapping wavelengths only make the colour.
You might have seen a rainbow at times also at the edge of the sapphire glass of your watches as a refraction (the layman would say reflection) that is hitting your eyes only.
The "canvas" for this light is your eye.
The moon disc here is the "canvas" for the refraction and therefore it is visible, "projected" on the moon disc,
Have a look again and if it is more like mother of pearl than the theory of mother of pearl can be reason.
Best
Moritz