Generally the trait of agreeableness is composed of factors that would go against the narrative of TRP or serve as a buffer. Trust, altruism, sincerity (i.e. not playing games, being upfront/straightforward), tendermindedness, modesty, cooperativeness-compliance. I do not remember the study, but the quote from below can be used to retrieve it.
"...positively associated with hostile attitudes towards women, sexual objectification and rape myths, even after controlling for personality traits such as agreeableness."

Basically, it seems to work as an ideology instilling beliefs, rather than an expression of character. This is a problem in the sense that it might be harder to spot a man who believes in TRP, but at least it shows it is not irreversible, and that it can be prevented, as it functions as an ideology.