[1] https://www.pbs.org/newshour/nation/transgender-kids-tend-to...
[2] https://www.thelancet.com/journals/lanchi/article/PIIS2352-4...
This is quite clear to me and I do not think gender dysphoria - which is a DSM-5 diagnosis [1] - is the correct term to use. Compared to previous years or decades (or centuries) there is a markedly higher percentage of children/young adults who "self-identify as 'trans'", often clustered and in waves. This did not use to be so but that does not mean similar phenomena did not occur, they just did not get a diagnosis attached to them. It is highly probable (and feed for a dissertation if there is a university which would accept such a politically charged project) that the same character types who now "self-identify as 'trans'" were those who would style themselves as "goth" or "emo" or (in the late 80's and 90's) "metrosexual" or any other androgynous style. The difference is that these earlier style figures did not come with a diagnosis nor were they adopted by any mainstream political movement and as such were taken less seriously. You could be a goth just like you could be a metalhead or a prep and be part of your in-crowd by just wearing the right clothes (and, for some crowds, make-up) and listening to the right bands. It was accepted as a way for children and young adults to "belong" without coming with much baggage.
[1] https://www.psychiatry.org/patients-families/gender-dysphori...
I don't see how you could usefully extrapolate a "real" baseline rate based on what prior generations did. Atypical sexual/gender identities have been taboo for almost the entirety of human civilization, and only as these taboos are now being lifted are people able to express these traits without fear of horrific repercussions.
I have seen this firsthand on some acquaintances. Social media has a massive influence on people and there are some persons specifically that have a weaker sense of identity (usually associated with poor development or some mental disorder like schizophrenia, STPD, or BPD), and those persons can be influenced to the point of actually, legit molding their own identity by their own media consumption.
This consumption in most people only plants seeds that will lead to questioning or trying stuff, but won't have a long-lasting impact on their core identity. So for most people this kind of exposition will be something either transitory or will just provide awareness. People grow out of it and it actually it's "just a phase" for many.
So yes people can learn to have a new identity if they don't have a strong core identity formed yet or if it is weak or broken enough.
OTOH, i am unsure what do you mean by a statistical over-representation of GD. There are no bounds set for deviation of the norm for the general population (i.e. normalized rate of growth of % of population that is transgender is not an outlier vs the rate of growth of other emergent behaviors afforded by greater overall inclusion and reduction of discrimination). The places where it is statistically over-represented, like on people within the Autism Spectrum, are under investigation.
In any case the risks of social media brainwashing are not restricted to stuff like disorders but go way beyond and i think the solution to this stuff is, like for many other things, more education and awareness of risks, tradeoffs, what is gender, what is identity, and how they work both intrinsically and within the bounds of social interactions.