There's tendency on the left (though not exclusive to it) to select fringe right-wing figures and project them onto the right as a whole. Fred Phelps, the "God hates fags" preacher, is an earlier example. The logic goes that these figures were saying out loud and offensively what the rest of the opposition to gay marriage were thinking privately. There can can sometimes be an element of truth to that. Clearly, during the 60s and 70s, when it suddenly became impermissible to be visibly racist, many people still harbored racist views and a figure like David Duke articulated them publicly.
But in the case of gay marriage very few of those who opposed it agreed with polemics Phelps, even privately. Harping on Phelps obscured the debate that was much better characterised by the positions of David Frum vs. Andrew Sullivan and the left and main stream media didn't serve the public well by constantly platforming Phelps, which was surely his goal with his brand of outrageousness. The left, IMO, has become addicted to using strawmen rather than debating real issues. Everyone is a Hitler. Everything is racist. The trans debate captures this tendency in its extreme form: Jim Crow, segregation, racism, homophobia, misogyny, genocide, apartheid, Christian intolerance, white supremacy, patriarchy, ableism, body shaming, conversion therapy, and eugenics have all been invoked to shut down conversation about the subject.
With the case of women's right to vote, the phenomena been noted on Mumsnet, that very often the most dogged supporters of trans rights within captured organisations are women, who often subordinate their very considerable responsibilities to supporting trans rights above all other priorities. Why? And what's to be done about it? Obviously the answer is not to take away women's right to vote. That's very silly. But articles like this associate anyone making that observation with an extreme form of active misogyny. Note how many imply or explicitly claim that SexMatters is a front for right wing (American) Christian extremists.
In fact one can detect why there might be a self-reinforcing dynamic at work here: if being against trans rights == being against women's right to vote, then of course the stakes are much higher for defending trans rights, as transphobia becomes the thin edge of the wedge to disenfranchisement.
Edited