Regardless the GOP is not a "cabal of men in America forcing women to behave in certain ways". Even if they believed that (I don't think all republicans do) they in no way have the authority to "force" women to do anything. Abortion is legal in the US.
Also GOP != patriarchy.
I never said GOP = patriarchy. Just that there is a "systematic, coordinated campaign against women's reproductive rights" and that certainly isn't a fringe statement. This campaign is indicative of one of the OP's definitions: "interwoven social structures that promulgate certain ideologies, doctrines, and social customs."
You're really stretching the original comment to try to make it less extreme.
A group, the large majority of are male, are trying to limit what a women can do with her body. The same thing the OP said.
1: http://www.nytimes.com/2015/06/02/upshot/gop-women-in-congre... 2: https://en.wikipedia.org/wiki/War_on_Women
While I can't find good figures on male/female split in the GOP, the fact that the US has overall a slightly lower than 1:1 male/female ratio [0] and the fact that women are substantially more likely to identify with the Democratic Party than the Republican while (including leanings of independents in both cases) men are about equally likely to identify as Republican as Democratic, suggests that that presumption would be wrong.
[0] https://en.wikipedia.org/wiki/List_of_countries_by_sex_ratio
[1] http://www.people-press.org/2015/04/07/a-deep-dive-into-part...