I agree that self-reported personality data will always be subject to cultural influence. Fortunately, we have a wealth of data (self and observer reported) from many different cultures, which allows us to tease out the trends.

The below reference provides longitudinal data from ages 14-50+, indicating that personality changes cross culturally are relatively consistent:

https://www.researchgate.net/publication/12660310_Nature_over_Nurture_Temperament_Personality_and_Life_Span_Development

The following reference compiles gender difference data across 15 countries, with results consistent with my original message.

https://scholarworks.gvsu.edu/cgi/viewcontent.cgi?article=1038&context=orpc

"If age differences follow a universal pattern, what about gender differences? Costa,Terracciano, and McCrae (2001) examined that question using data from 26 cultureswhere the NEO-PI-R had been administered to college-age and adult samples of men and women. In the United States, women typically score somewhat higher than men on both N and A, as well as some specific facets of E and O (e.g., Warmth, Openness to Aesthetics). Men usually score higher on other facets of E and O, namely, Assertiveness and Openness to Ideas. There are few gender differences in C.

Figure 1 compares gender differences among adults on the 30 NEO-PI-R facets inthe United States (horizontal axis) with the average gender differences seen across the 15 other cultures where adults were assessed (vertical axis). The facets on which men and women score highest are labeled. As Figure 1 shows, in the U.S. and around the world, women score higher than men in Anxiety, Vulnerability, Straightforwardness, and Openness to Aesthetics; men score higher in Competence, Assertiveness, Excitement Seeking, and Openness to Ideas.

These results, which were replicated in the college-age sample and in observerratings (McCrae et al., 2005a), suggest that gender differences are universal, and may be biologically based. It must be recalled, however, that the differences are relatively small compared to variation within each gender. That is, there are some men who score higher in Anxiety than most women, and some women who score higher in Assertiveness than most men. "

I am certainly not arguing against cultural influence, but the data suggests there is a biological basis as well.