While I get the analogy with Muslims versus Islamicists (and indeed it's one I frequently think of myself in reminding myself that most of the transwomen in real life, the people I know, the people like Miranda, are moderate and sane), there's an important disanalogy. In the case of trans issues it's as if the extreme Islamicists were driving the legislative agenda. Issues like insisting that transwomen should be allowed into women's prisons even if they've been convicted of raping women and female children. Issues like insisting on self-identification in the face of opposition from the professional body of psychiatrists who work with prisoners, pointing out that self ID can and will be misused by violent men pretending to be trans in order to gain access to literally captive pool of vulnerable women. And like extreme Islamicism, it raises heresy to the status of a crime, in having laws against misgendering, up to and including not knowing the 57 flavours of gender like zie and hir (everyone, learn your catechism and repeat it to the priest).
I'd be all in favour of sane laws saying that no-one should lose out on the 99% of jobs where biological sex doesn't matter, or be harrassed out of their housing, for being trans. I'd even back making it a legal requirement for businesses to make reasonable adjustments - e.g. a gender (sic) neutral toilet.
I can even understand the distaste with "gatekeeping" - I have a degree of sympathy with people who say "why should 'the way you are' require a medical stamp of approval?" But there needs to be some sort of checks and balances to prevent the end result of people - any people, whether trans or pretending to be trans for personal gain - self ID-ing to get into a women's shelter, prison, or suddenly, as a mediocre male athlete, finding themselves with the prospect of a glittering and unusually middle-aged career in women's sport.