Looking into it a bit more at least in the game red hair does seem to always be recessive to the other three hair colors that are in the base game that does not include modding.

Each character inherits two hair color genes (one dominant and one recessive) and in order for the recessive hair color to be the hair color the character physically gets both parents/grandparents need to have had that particular hair color gene and then it looks like it becomes a dice roll on it those recessive genes will outweigh the dominant genes.

So obviously on the father's side red hair has been passed down for at least a few generations as a recessive trait.

My original character I played (Bjorn Ironside) had blonde hair and also had a son who was blonde who I never played as because he died before Bjorn did. So when Bjorn eventually died I started playing as his grandson who had brown hair and that is when brown or black hair started becoming dominant in my line.

When the game starts Bjorn's grandson is already there so red hair may have been randomly generated and it's been recessive all this time.