It's funny how this entire argument… discussion… whatever you want to call this is one long string of unpopular opinions.
I think there are two primary ways that people who spend far too much time online "see themselves" in fictional characters. I know this, because I myself spend too much time online :)
Type 1 are your Patrick Bateman/Ryan Gosling/Joker types. They see aspects of themselves and their struggles in these cool characters, and because these characters are cool, they decide to try and emulate them to some unironic degree. These characters also tend to be very sympathetic villains for whatever reason; there's probably some deep psychology in there, but it's past midnight and I don't care. This also applies to "girlboss" characters, but less often, because they tend to be more hollow (again, for some reason). This is basically an updated conception of "fictkin", but for those on the sigma grindset.
Type 2 are your Brisket/Spider-Gwen types. They see aspects of themselves and their struggles in these popular and pretty characters, and because these characters are popular and pretty, they decide to project their own identity labels onto them. Lore doesn't matter, only that they're popular, pretty, and in some way don't conform to a rigid conception of gender roles (and they need to be likeable; I've never seen this happen to Ash Crimson, who's quite girly and flamboyant, but also a total dick). This isn't exclusive to trans people, but with them it is the most persistent; the same thought patterns are much harder to sustain when applied to skin color, physical disabilities, or severe mental illness. In many ways, this is a rebirth of the old "shipping wars"; both predominantly involve foreign media, blorbos, spurious evidence, and colossal flamewars.
These different types have different manifestations: Type 1s seem to mostly use the medium of fancams, whose biggest sin is showing up too often in meme compilations. It's annoying chuuni shit, but easy to ignore if you don't like it. It helps that most people who really like these characters are already like this, so few toes get stepped on by a deluge of sigma memes.
Type 2s are much, much more varied, scaling everywhere from "shitty fanart that ten people ever see" to "literally vandalizing the Wikipedia article for Samus Aran". Being more prevalent, involving far more characters of much broader popularity, and having been around for much longer, it's very hard to avoid and easy to get annoyed by, especially given the sheer propensity this has for causing drama.