Like with many other stereotypes, there is some truth and there is some myth. Let us begin with the myth part. The notion that all or most or a majority, or even a sizable minority of people in Ireland north and south have red hair is a myth. Red hair is associated with the gene MC1R, a recessive gene and somewhat rare gene. It is estimated that only about 2% of the world's population have red hair and a somewhat higher number do not have red hair but carry the relevant gene and may therefore pass it on to their children. It is unusual but by no means rare for a husband and wife to have dark hair but being carriers of the gene to have a child with red hair.
So much about the myth part of the stereotype. But what about the truth part of Irish red hair? The truth part is that although the majority of Irish do not have red hair, nonetheless, the incidence of red hair in Ireland north and south is much higher than in other places. We noted above that taking the population of the world as a whole, about 2% have red hair. In the US the percentage is estimated at around 2% though some claim as high as 5% or even 6%. Europe seems to have the highest solid concentration with around 4%. Scandinavia is somewhat higher than the European average and the Mediterranean countries lower. However, the highest percentages are in Scotland and Ireland with percentages above the 10% mark. Some reports put Scotland slightly above Ireland and others put Ireland ahead. Behind these two ranks Wales and Cornwall.
It is obvious that the incidence of red hair in Ireland is 5 times higher in Ireland than in the US or the rest of the world, and 2.5 times in Ireland than in the overall Europe. The stereotype therefore, does have a ring of truth to it.