The trans movement got so far because mainstream society needed an answer to the tensions raised by the SJW movements of the 2010s. The mainstreaming of feminism, BLM, gay rights, ableism awareness etc. etc. all contributed to a cultural shift whereby the average person had to have 'good politics' to be seen as a good person, rather than merely being well-meaning with good manners. The right-wing response to this, as we all saw, was to go completely bonkers, accidentally revealing how much politics and good-person-ness have always been intrinsically connected. Basic kindnesses like mask-wearing were heavily politicised, because the right-wing were backed into a corner: suddenly, simply saying 'I'm not racist' wasn't enough - you had to actually be not racist. Your politics wasn't some separate side issue, anymore: it became directly tied to your morality - your public-facing morality at that. Mask-wearing is a public-facing expression of morality, and that was the straw that broke the camel's back for a lot of people.
The thing is, as well-meaning as the left-wing is, nobodies' politics are pure, and everyone wants the safety net of being seen to be a good person without actually being a good person. Being a good person - being actively considerate at most if not all times - is hard. And even more hard is having good politics, because it requires deep thought, careful consideration, constant reflection, and a decent chunk of humility - and, at its core, it requires some sort of desire for the destruction of hierarchies and the reconstruction of society. The left-wing has a lot of oppressors in it - white people, straight people, men - who ostensibly appreciate the mainstreaming of good moral politics, but ultimately do not wish to sacrifice the privileges they have.
So, then: we have a tension between what is required of us, and what we subconsciously want. Trans politics got mainstreamed fast because it's an axis of oppression that everyone can easily claim to recognise precisely because it doesn't exist. It costs zero reflection to say 'he, she or they' - and bonus points!! it actually evades any recognition of, and reflection on, axes of oppression that actually do exist: sex, sexuality, even mental health and intersex conditions. Given how misogyny is the oldest, most widespread and most deeply conditioned oppression in human history, feminism - even the most milquetoast, sex-positive brand of feminism - was causing major cultural tensions. We had the first wave of backlash with gamergate and 'sexist air conditioning', and feminism has majorly backtracked since then, embarrassed and desperately seeking to curry favour with the oppressor class. Trans activism has been championed by mainstream feminism as an apology, and it's entered mainstream culture by storm for the exact same reason.
In addition to that, a cultural interest in 'heartwarming stories', a background of individualism, and increasing capitalist consumption as a form of identity, have all contributed to the trans narrative nestling comfortably within our culture. Think about it - the people least affected, least involved in the discource, and the most safe from heavy criticism - are men. White, 'cis', straight men. The top of the oppressor tree, if you will. But it's women who are getting the flack. Lesbian women especially. Trans politics has been a perfect response to feminism, a perfect response to basically all real-world politics because anyone who wants to have their relationship with their oppressor status can simply start going by they/them pronouns, at which point we're not supposed to talk about their relationship with their biological sex or how they were treated growing up. Both these things are the absolute bedrock of feminist theory, and both are lost when you try to be trans-inclusive. Transgenderism has provided the perfect political smokescreen to obfuscate power relations - it's the perfect liberal politics, one where being 'good' and having 'good politics' means letting people do whatever they want without criticism, even theoretical criticism. Now even your average normie is talking about nonbinary people - and I can tell you, these people don't know what nonbinary really is. Nobody really understands what gender is, but that doesn't matter, because it comfortably reinforces 'dress = girl' and now everyone gets to feel progressive without having learning anything.
