I’d never heard of the whole “never wash your hair while you have your period” thing so googled it to see where it came from.
One of the first results was a two-year old article from a website called Daily Hunt which reads-
Menstruation, or period, is a common procedure for women every month, in which dirty body blood is released. This is the reason that women are asked to take good care of themselves during this time. At the same time, it is advisable not to wash hair during periods, but nowadays women consider it wrong and wash their hair, which is wrong. Today we will tell you whether to wash hair in periods or not ...
In such a situation, if you wash your hair during your periods, it will cool the body temperature. However, during periods, the body needs to be kept warm, so that the dirt of the stomach gets cleaned thoroughly. In such a situation, the body temperature decreases by bathing or washing hair during this time, due to which the dirt of the body is not able to get out well.
Not only this, slowly this filth becomes lumps, which can cause cancer in addition to diseases related to the uterus. Bathing or washing hair in periods does not completely release the toxins, causing infection. Chances of problems like intense pain increase. So do not wash hair for at least 3 days. You wash your hair during the last days of the period. If you cannot avoid bathing and washing your head during this period, then use light lukewarm water for this.