Two things really annoy me about Hadley Freeman's piece, suggesting she doesn't understand much about either side or party in the US.
Describing Ted Cruz and Republicans generally as "misogynistic" for opposing abortion is an idiotic calumny. Pro-lifers view abortion as the taking of human life, and many, including many women, consider it unconscionable in most circumstances. No-one wants abortion banned out of hatred of women. By calling sex-realists "misogynistic," Freeman debases the term (which is dumb when you are facing actually misogynistic "biology-denying, rapist-pandering cultists") and is being just as high-handedly dismissive of Republicans as she accuses "gender ideologues" of being toward "feminists."
Second, Freeman excuses those same cultists by suggesting they are accidentally stepping on rakes. From the nominee Sarah Netburn to Joe Biden, these people are true believers. Netburn did not make an error placing a rapist in with women due to a "shaky grasp on the facts." She defended herself doing so, and would do it again. The Democrats in power are not "accidentally" doing anything, it is what they believe. They are exactly as irrational as they appear.
And in fighting against the true believers, you will need all of the allies you can get.