Aisla, you make some excellent points (and no, I don't consider your earlier post to be overly critical). You wondered what the writer's point was and it occurred to me that the article, though well-intentioned, doesn't have much clarity or substance. If we have to wonder what she's getting at then she hasn't communicated effectively and she's losing us.
That said, the transgender "umbrella" (and yes, I used scare quotes) is probably dead, but not for the quasi-political reasons that this blog (and the ones it links to) say it is.
The beauty of language is that it's a living thing, constantly evolving and acquiring new words to more effectively communicate what matters and discarding words that no longer serve a purpose. Sometimes those words evolve to become more meaningful to the society that uses them. Note that hardly anyone uses the word "gay" in its original sense these days; same for the word "queer".
The word transgender is evolving as well. Many people I know who would otherwise be covered by the "umbrella" (again with the annoying scare quotes) are pushing back. My crossdressing friends hate the term transgender because to them it implies transsexual and they're quite happy with their birth genders, thank you, and have no desire to be lumped in with anyone else in the gender-variant spectrum.
I think that is a situation borne of the media's use of the term transgender as, well, as an umbrella term, and they did it because we did first. Here it was, an excellent generic term that actually didn't annoy the people whom they referred to when using it, because they invented it! But like it or not, the generic term was used most often when covering stories dealing with transsexual people and thus the term has become conflated to be a description of someone in gender transition instead of just any gender-variant state of being.
So we're a victim of our own success. The term is still valid but its meaning is evolving, and only time will tell if it evolves into something useful or becomes passé. Either way, the "umbrella" (last time with the scare quotes, I promise!) is becoming less useful and merely an archaic appendage to the term transgender.
Sure, the umbrella is dead, but let us not mourn - it died peacefully in its sleep.