Nope, minger just means an ugly person but rhymes with singer.
I understand what you are saying and I’m thinking there are “striking features” and striking features. Perhaps features of classical beauty, as interpreted by culture, are remarked upon in a way which would be perceived as complimentary. (Although the frequent repetition could become tiresome.)
Then there are the features which are considered out of the ordinary or perhaps, “not of us.” I believe red hair is the least common of the variety, and as such, having it pointed out by others may imply a certain amount of alienation.
The history of persecution of red-haired people may suggest the same.
For instance, my first kiss was delivered to me by a lifelong friend with red hair and freckles. When I say I was once loved by the red-haired, freckle-faced kid, there are knowing smiles that I doubt I’d receive if I said I had been kissed by a blond, blue-eyed kindergartner.
What that unspoken something is is hard to say.
Perhaps discrimination IS too strong of a word, depending on how you define the word. I do believe in American culture, though, that there is a certain Tom Sawyerish, naughty boy impression that accompanies the thought of a red-headed little boy.
But with the stereotype there is also the singling out from the norm which is one marker of discrimination.
The most common explanation of this idiom is that the child couldn’t be mistaken for the step-father’s kid, and suffers for it because s/he both sticks out and is unwelcome. Definitely not a comment about the child’s temper.
Your cite includes both of these explanations, among others, so I’m not seeing how it proves it’s “definitely not” about the redhead’s supposed temper. The idea that the redheaded child couldn’t be mistaken for the stepfather’s natural child doesn’t make much sense either. There are any number of other obvious ways a child could fail to resemble his or her stepfather, including having any hair color not the same as his. Since red hair is a recessive trait, it’s common enough for a redheaded child to not have a redheaded parent anyway.