No, gingers are not going extinct. This myth has been perpetuated by the idea that those carrying the recessive gene won’t have kids, and therefore the gene will disappear.
That’s highly unlikely as there are more people who carry the gene, than there are actual people with red hair. As we know, red hair typically skips a generation.
The best looking girl I ever dated had red hair, i blew it big time with her. Still bitter about it.