Wasn't this all covered in Pluralus' introduction, including the phrase, "Someone inside a particular group can speak best about their own feelings and lived experience"?

It seems like you're arguing a point that Pluralus already granted.

The only question is how common the fallacious usage is vs. phrasing establishing presumptively relevant status, for which neither Pluralus nor you are providing any solid data.

I searched "as a white woman" on Medium. Of the first 18 hits, I count two that are simply referring to a role played by someone else (e.g. acting), and 16 that establish self-identity. Of identity claims, four were made for self-effacing purposes (basically apologies for being the wrong identity group), one was used to claim take-my-word-for-it style authority in an empirical matter, five were about personal experiences offered as examples of white-woman-type-experiences (note: this included two that were polar opposites from each other, illustrating the limitations of lived experience as an individual member of an identity group), four were made to claim social credit (I'm one of the good ones because I'm outraged about this issue), and two were talking specifically about how to handle identity issues.

So at least for the "as a white woman" category, at least on Medium, at least as Medium decides to present it to me using whatever magic sauce it uses, Pluralus' characterization is substantially correct. I intentionally picked an identity category that has aspects of both "privilege" (white) and "oppression" (woman), but it turns out at least on Medium-as-shown-to-me, this sampled reacting to privilege-stereotyping much more strongly than being-oppressed.

Anyway, bottom line is that, especially given the caveats in the OP, Pluralus seems to have a pretty solid point here. (This doesn't make your point about common experiences wrong--it just means that your arguments do not show that Pluralus' thesis is predominantly wrong.)