There are certainly people making money from this. And I expect a number of them are doing so cynically and unscrupulously. They are simultaneously exploiting a situation, and in doing so pushing it further.
But that is not proof of a grand, big conspiracy.
The idea that population control is behind this is particularly ridiculous; if you wanted to limit population growth, there are far more effective, more efficient, less complicated ways to go about it than targeting a small percentage of a demographic that typically doesn't have large families anyway, within countries where small families are the norm.
The main reason why big, complex conspiracy theories often collapse when I look at them closely is not because I doubt the capacity of humans to have sinister/evil aims, its because they always seem like a ridiculously difficult means to that aim.
The world is so complex, and it consists of so many interconnecting, complicated systems. Plus, those systems are shifting all the time.
It is almost impossible to predict how a particular action on one part of the system (say funding a TRA group) will have on another (say, population growth). However, it is (comparatively) easy to stir up shit- because you don't need to know exactly what effect your shit stirring will cause, you just need to know it will cause a bit of chaos.
So I think there is a bit of that happening on social media. There are also some unscrupulous individuals who have spotted a great way to make money, some attention seeking people who have found a great way to be in the public eye, some power/popularity seekers who think they are aligning themselves with public opinion, some sexual predators who have spotted a great way to access what they want/a literal get out of jail card, some people who think they are supporting a just cause, some people with MH difficulties who think transition is a panacea to their problems, some misogynists who instinctively sympathise with pink-brain-blue-brain-bollocks, some who aren't yet really fully aware of what they are supporting, and some people who are just thick.
This rag tag mob may not be very large relative to the population, but they are disproportionately loud and some of them are influential/powerful.
Couple them with the majority of the population who are as yet unaware of what is going on/don't care/too scared of potential repurcussions to not tow the line, and you get this weird situation which appeared to spring up out of nowhere overnight (I don't think it did- mouldy apples and all that).
If you want an analogy for how this took hold so fast, I think that previous civil rights movements are the wrong analogy. Look instead to cults, and even social awareness over issues like veganism, plastic waste etc, which can grow from a small base to a large one very quickly - there's a sort of positive feedback loop at play sometimes. Sometimes this is positive (pubic awareness over plastic etc) and sometimes negative (cults etc).