I have been involved with several discussions about trans vs. trans*, genderqueer, non-binary as terms to refer to people who do not identify with gender normative maleness or femaleness.
Some people who do identify this way feel strongly that trans should be the only term used. That by using different words like trans*, genderqueer, non-binary we a) reinforce a gender binary and b) buying into the term trans only being for binary transgender folks.
Mostly recently I was told off for using 'trans/non-binary' because, according to that person, making a distinction between trans and non-binary assumed there was a gender binary.
The thing is, as much as I wish it were otherwise, that assumption has already been made. Our society functions on an assumed gender binary. The very concept of heteronormativity and assigning someone a gender at birth depends on it.
Refusing to acknowledge something -- even a wrong something -- does not make it go away. In fact in the case of the gender binary we've seen the very opposite to be true. Not talking about, acknowledging or questioning it is the very thing that allows society's concept of a gender binary to hold so much sway. By taking away language for talking about the people outside of it, we take away some of our power to address and critique it.
I also know how it feels when a transgender person says that trans can only be used by transgender people who understand their identity in a very specific way. I know the feeling of having your identity denied by the entire world, only to have it denied again by the community that should support you. I know how it feels to have other trans people tell you that you are not trans enough or even that your identity is somehow transphobic. I totally support those people who's response to that is to grab hold of 'trans' and refuse to let go. I may in fact at this point count myself among those people. But I know that's not everyone's reaction and there are still people who need/want other words.
I am pro people using trans with or without the asterisk as an umbrella terms for all none cis people. I am also for people who do not identify with a binary gender identifying as trans. I just think we make more problems than we solve by erasing all other possible words. We also run the risk of erasing words people might identify with just because we, ourselves do not identify with them.
I personally have a long and complex history with using the term 'trans' as applied to myself. Although I am becoming increasingly more prone to using it I usually do making the distinction that I am a trans, non-binary individual. And there has also been long stretches of my life where I've been far, far more comfortable self-identifying as genderqueer, non-binary or trans*. Not because I want to enforce the idea that trans can only be used by binary transgender people, say that there is only one way of being transgender, or enforce society's, very harmful, notion of a gender binary. Instead my use of these words comes from my own (and ever changing) relationship to my body, my gender and language in general.
Bottom line is I do tend to use trans/non-binary when referring to the full spectrum of none cisgender people and will probably continue to do so. Because I think trans as a term is important but I want to be sensitive to the large portion of the population who are not cisgender but do not identify themselves as trans either.