My theory about how this all began is that most people saw it as Act II of the gay and Lesbian struggle for equal rights and never spent much energy on trying to think all the consequences through.
(It's actually quite complicated because of the way words are now being used whatever the speaker decides they mean, because the underlying theories contradict each other, and because most people don't realise that 'gender identity' does NOT mean just accepting the label 'woman' or 'man' for just being female or male, respectively, but full allegiance to the religion which believes in gendered souls floating in empty space and randomly attaching themselves to various bodies.)
So people wanted to be kind and 'on the right side of history' and to be seen as virtuous, and most who had any qualms told themselves that it's only a tiny percentage of people and won't affect anyone else's rights.
Three further things then pushed the development further:
One was funding and support from the moneyed top layers of societies. No other social justice movement has ever had so much money so fast! This access to plentiful funding meant a well-oiled machinery of activists which quickly gained influencer positions in organisations, when combined with the general desire to be 'kind'.
The second was the political acumen of the movement and the skills it has exploited:
Tying its goals to other social justice initiatives, such as same-sex marriage, to get them passed without public debates, working behind the curtain as much as possible, creating a set of easily remembered mantras disseminated everywhere, and exploiting data from, say, Brazil, to suggest that homicides of transgender people are more common than homicides on average in the UK, the US and Canada, say, when, in fact the opposite is true in all those countries.
When this is combined with the plentiful funding we get Stonewall indexes and other similar incentives for corporations not to dig too deep into anything.
The third aspect is, sadly, the fact that almost all negative consequences from the most fervent demands of trans activists only hurt the female sex class. The male sex class is mostly unaffected, and so men have the luxury of being seen as kind and virtuous without actually sacrificing anything.
I have learned, from this whole debacle, how a certain kind of widespread contempt towards women is what drives much of this:
For example, it is the pain of trans athletes which we are to prioritise, not the pain of the female athletes who lose their chances of winning places on the podium or money prizes for some competitions or athletic scholarship from inclusiveness, and it is also the case that inclusiveness demands have almost entirely been aimed at only the female sex while the male sex has, until very recently, been left alone. (No 'impregnating parents' suggested for fathers while mothers are in some places now called 'gestating parents.')