This is stupid, there is ZERO logic to this. You only need a basic knowledge of how cancer works to work this out. If anything, you should wash more during your period. This is complete and utter rubbish, ANY medical professional will tell you that everything you do when you aren't on your period, you can do while you're on aswell.
I don't see how any fair and unbiased research could even come to this conclusion regardless of the culture.
Cancer is mutated cells dividing and growing out of control and dividing and spreading first locally throughout the body. How exactly would washing your hair, on your head during your period, which happens in your reproductive system, cause this? Which cells are being put at risk of mutation here? What sort of cancer are you supposed to be able to get??