I think the association with red pill is probably because men in general read much less than they used to, and the books men do read tend to be nonfiction self-help.

However, How to Win Friends was written in an era where self-help didn’t have those connotations at all.

There is probably some deeper relationship with current reading trends and contemporary winner-takes-all society, but my impression was that the book was more about middle class aspirations e.g. being charming at a dinner party. Not some kind of Machiavellian social maneuvering like 48 laws of power (“crush your enemies completely”).