Global intermingling, which broadens the availability of possible partners, has reduced the chances of redheads meeting and producing little redheads of their own.
It takes only one red-haired parent to produce ginger-headed babies, but two redheads obviously create a much stronger possibility.
Hm? Apparently they don't understand basic genetics. Red hair is primarily caused by one gene, red/not-red where red is recessive. So a parent with rr will have red hair and a parent with Rr or RR will have not-red hair. However, if parents are simply carriers for the gene, Rr and Rr then a solid 1/4th of their children will have red hair. It actually takes zero red-haired parents to produce a red headed child. Secondly, ginger is blond+red whereas auburn is brown+red controlled (pretty much) by the two genes. And blond is recessive. So frankly, if the genes get mixed up into the population then you can still produce a ginger from two dark haired individuals. In fact, have the same number of genes would exist simply mixed up into populations that don't express the genes. It would not make the genes less frequent.
Genes are a pretty simplistic idea of what's actually going on to express those traits, but really... this one fits the model really well. And even then they don't seem to get the model. That or are using "extinct" to mean a decrease in typical phenotype expression.