No. Redheads are here to stay and you shouldn’t believe everything you read.
In the early 2000’s it was widely reported that the redheaded trait would die out, and this could happen as early as 2060.
The reason cited was that the gene for red hair is recessive and thus would be eventually be eliminated from the gene pool. This reasoning incorrectly assumes that in order for the recessive red hair gene to be passed on, both parents must have red hair.
As a person of the redheaded persuasion myself, I can report first-hand it is not necessary for even one of your parents to have red hair.
The only requirement needed in order to pass down a chance of having red hair is for both parents to carry the recessive gene responsible for red hair.
Similar predictions of the extinction of blue-eyed people have circulated for many years. For all the same reasons, that prediction is unsupported by facts (fake science news!).
Under what conditions could this be true?
Well, there is one scenario where redheads could go extinct. As much as we like to believe we’re invincible, it is very likely that if the human race were going extinct, we’d probably go too. We’re special, but maybe not so special that we’d be immune to human extinction.