For example:

Recent studies have debunked the idea that women's sexual preferences change based on their menstrual cycle. Yet many Red Pillers still cling to the idea.

https://datepsychology.com/why-dual-mating-hypothesis-research-has-failed-to-replicate/

Red Pillers say that women are solipsistic and men are empathetic. Yet many studies show that women are more empathetic than men.

https://www.webmd.com/balance/news/20230103/females-are-more-empathetic-than-males-study-confirms

Many Red Pillers say that women's self-esteem is too high and that they need to be knocked down a peg. Yet men have a higher self-esteem than women.

https://www.apa.org/pubs/journals/releases/psp-pspp0000078.pdf

Red Pillers imply that women cheat more than men. Even this appears to be untrue.

https://discreetinvestigations.ca/infidelity-statistics-who-cheats-more-men-or-women/

Many things TRPillers say are misleading or untrue. I think if TRP works for you, it's fine. But many Red Pillers act like TRP is some "objective, scientific truth" when it's not. TRPillers should admit it's just what intuitively sounds good to them, not science.