Rest assured, I am quite able to be disagreeable without need of internal contradiction. My statements, in any case, are not contradictory. "For F women and T men, cultural conditioning reinforces innate tendencies" applies to contemporary U.S. society, and applies regardless of the proportions of men and women who are T and F. "Culture often follows the tendencies of those in power" is a general statement about societies that often plays out over time. When the imposed culture is significantly different from that of the majority, culture clash results. This is the situation documented by Eisler. Will a given individual follow the familiar, "native" culture, or the ruling culture? The answer to that question may itself be type dependent. In contemporary society, the ruling culture and the majority culture substantially coincide since any significant clash is in the distant past. Culture thus reflects not so much the innate tendencies of the majority, as the tendencies that the majority has been programmed, even bred to exhibit.
Regarding type theory, I was referring to the distinction between functions (N/S, T/F) and attitudes (E/I, J/P). Whether or not these terms are used by Jung, they are used in a number of MBTI books and articles. This is a separate question from asking whether the dichotomies are bimodal or continuous. The reference you linked is interesting, but by its own admission, does not resolve this question. It simply undercuts one argument used to support the bimodal distribution theory, by showing that the presence of bimodality is significantly influenced by how the questionnaires are scored. This is not surprising given the highly subjective nature of the topic. (It is interesting that this reference also criticizes prior studies based on college students for not using a representative/random population, but then gets its own results from managers in a leadership seminar. This population might easily be more homogeneous than college students.)
I have read more on the links between personality and physiology, specifically brain differences. The evidence so far seems most conclusive regarding the E/I scale, and suggests that the brains of introverts and extraverts are simply wired differently. See for example:
http://www.scienceagogo.com/news/19990228212951data_trunc_sys.shtml
Less conclusive but still tantalizing results link physiology with traits generally associated with the J/P distinction:
http://abcnews.go.com/Health/Healthday/story?id=4508869&page=1
Finally, some researchers have results that point to four of the "big five" traits:
http://pagingdrgupta.blogs.cnn.com/2010/06/22/personality-shows-up-in-brain-structure/
Some of these conclusions seem to go out on a limb a bit, but to the extent that personality difference is based in physiology, it might indicate a more bimodal nature of the distribution, as with gender and handedness. Yes, there are hermaphrodites and the truly ambidextrous, but these are small minorities.