Disclaimer: I am transgender and i have done actual research on transgenderism a couple years back.
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.