I should start by saying I personally love redheads, and I'm Irish by birth, and have a strong affinity to my celtic heritage. I believe none of the things I am about to write about redheads.
I have wondered however if the way people jokingly talk about redheads has anything to do with a celtic association from Rome's celtic wars that's carried through to modern day. That redheads are soulless, quicker to anger and somehow evil, or if it came later through perhaps how England viewed the celtic nations. Was this some kind of racism that would be akin to how any people with distinguishing features seem to be treated in wartime even today, for example how Asian people were treated by some in the US during WWII and vice versa, or how people of middle eastern extraction can be treated today?
That would be too logical.
Various cultures have had superstitions about red hair, some positive, some negative. (Redheads have always been uncommon. If the only redhead that you know does something unusual its easy to overgeneralize into thinking that there is a a cause and effect relation.)
There IS a phrase "Red Headed Step Child" that has been around since the mid 19th century. It refers to a child that looks nothing like the father which hints at some degree of questionable paternity. This phrase is often used metaphorically to indicate a junior ranking person or a subgroup of an organization that does not get much support from those in charge.
I personally think that a lot of it comes from a South Park episode where one of the characters insists "Gingers have no souls". Due to subreddit rules we will not be able to discuss this until 2025.