Critics (The Washington Post among others) were quick to point out that the so-called scientists cited by The Independent were dubious sources.
One refused to be named, and the other is not a geneticist (nor any kind of working reputable scientist).
Read: Redheads feel more pain
What's the real redhead story?
The "redhead extinction scare" is a myth, and it's hit the news before. In 2007, The Courier-Mail ran a similar story, also not backed up by reputable genetics or geneticists.
It's true that redheads have the rarest hair colour, and, proportionately as the world's population grows, there will likely be relatively fewer of them in future. Even so, there's no evidence that the genes for red hair are on their way out.
Red hair occurs in populations distant from those that have high numbers of redheads like Scotland. Also, people may carry the redhead gene but not express it; it's expressed in their children or grandchildren.
Redheaded girl, Kashgar, China (Wikimedia)
Pale skin and vitamin D
Sunlight exposure is an important source of vitamin D: our skins manufacture it. The redhead-extinction proponents cite the (established) theory that redheads came into existence because their pale skin allowed them to get enough Vitamin D in cloudy northern climates with little sunshine.
This would no longer be an advantage as skies become sunnier, say the extinction-theorists; instead, redheads will be more vulnerable to sun damage.
Read: The miracle of vitamin D
Pale skin, folate and cancer
Pale skin and eyes do put you at greater risk for skin cancer from ultraviolet (UV) radiation. Redheads have the highest risk; blondes and brunettes with light eyes and fair skin aren't far behind.
But there's no evidence that this might be a factor in reducing numbers of paler-skinned people in humanity's evolutionary future. Awareness of sun damage, and taking steps to avoid it like using sunblock, also mean skin cancer isn't an inevitability.
A more convincing theory from physical anthropology is the link between skin colour and folate, a vitamin essential for building DNA; deficiency can cause birth defects.
If pale-skinned people get too much sun, it can destroy their folate. Folate is very sensitive to UV radiation, and when it's carried in the bloodstream near the skin's surface, sunlight can destroy it.
Read: Your complete guide to folate
Not fading away: annual Redhead Day, Netherlands (Bart Rouwenhorst)
How we came to be different colours
But the evolutionary origins (and the evolutionary future) of redheads, and of skin colour in general, are complex and hotly debated.
Some scientists think that vitamin D and folate were important factors, and this does seem to make sense: skins are darker at the equator where the sun is more intense, and become paler as one moves towards the poles.
Read more: Why skin is different colours
However, other scientists think this explanation may be flawed, or at least over-simplistic. Recent research indicates that dark skin may in fact manufacture vitamin D much more efficiently than was previously thought.
What is your skin type?
Birds hold clues to why there are redheads
Red hair might raise melanoma risk
Hooton, C. July 2014. Gingers face extinction due to climate change, scientists warn. The Independent.
Sullivan, G. July 2014. No, climate change is not driving redheads to extinction. Washington Post.
Courier Mail. August 2007. Gingers extinct in 100 years, say scientists. Courier Mail.