As per what Cindy said about *rights, that's what it really comes down to.
The argument of trans vs trans* though, I find both to equally problematic. Hopefully I'm not about to start a full on FlameWar based on semantics but here's why I think both fall short.
In the Hetero vs Homo space, we don't use Homo or Homo* to include Bi-sexuals or A-sexuals. There was a movement to try to replace LGBT/GBLT/LGBTIQQ2A* with QS(R)M - Queer Sexual (sometimes Romantic was included) Minority. QS(R)M covers everyone without the inclusion being "lead" by one group or another (L or G?).
Vis-a-vis cultural whiteness, in the Western world anyway, there's no catch-all for the culturally non-White and the implications of that are for another day/post.
Also in the Western world, Christianity vs non-Christianity. Take your pick at rankings of Judaism, Islam, and all the others I haven't listed. And then if you want an extra layer of complexity, apply those rankings to people who have white skin.
Then if you follow Serano's arguments, the biggest rights battle is simply between masculine and feminine. And we're back to gender definitions again.
I like QSM more than LGBT variants as it's inclusive without preference. I like QUILTBAGS even more as an acronym as its got a lot more letters that fall into not-cis-hetero-typicality and doesn't have any actual breakout that I know of. And QUILTBAGS will never catch on sadly.
So, in that not hetero*, not-culturally white*, not Christian* sense, I think the terms fall short of defining a non-typical that doesn't exclude. I find it clumsy but "trans*/non-binary/gender queer/andro" statements in explicitly inclusive events a lot better than just either trans or trans*. Oh and from my programming background '*' is just a wildcard. I'm glad its use as a prefix (->-bleeped-<-, transgender, transexual) seems to be shifting to that of an adjective (eg trans woman, spanish speaking woman, etc).
Just the thoughts of a culturally white, perceived as cis, born Jewish agnostic, trans woman (aka just another human being,) who tries her hardest not to be a jerk about it as much as possible. (And sadly there are people who would limit who gets go be included as 'human' eg Nazis, witch-hunters, etc.)