So this is a different change than the one you were originally talking about, when you made the incorrect claim that 'For centuries, "they" has been plural and "he" has been used for gender-neutral singular third-person.' It sounded like you were proscribing the singular "they". There's no change in whether the singular "they" is a gender-neutral singular third-person pronoun, only the generic "he".
The singular "they" has existed throughout modern English. Getting rid of it is an insurmountably awkward and drastic change. People have tried, and they can't even remove it from their own speech.
The generic "he" is a relatively newer affectation that has risen and fallen in popularity in formal writing. I guess you can find a "PC crowd" to blame for its current decline, but this decline supposedly started around the 1960s, so you're not really observing anything new.
The only thing that's recent is (as EdiX pointed out) that there are people speaking out to say that they, as individuals, would prefer to be referred to with the singular "they".