Explain why neither the oil nor the glass fiber interferes with the diffraction pattern of the crystal.

It's because The oil and the glass fibers do not interfere with X-ray crystallographic measurements because only one is crystalline.

Glass fibers have a low absorbance for X-rays and is not crystalline. Because of this, glass fibers will not interfere with X-Ray patterns. Oil, on the other hand, could be considered as crytalline.