I don't feel that's quite true, much the same way I feel like the compromise (hey! let's shut down stuff in DC!) accurately represents the Republican bias against African-Americans and poor people, which similarly clearly exists.
A lot of the GOP doesn't especially hate women, but this situation like this is a no-lose thing for the entire party; they get to appear like they're standing up for their "pro-life" and "small-government" constituents while making Obama's administration look like the bad guys for nearly stopping budget talks. How could any ethically bankrupt person with no actual loyalty to their country as a community, possibly resist such an opportunity? I do realize that isn't better than accusing them of being misogynistic bigot scum.