Of course we do.
People without a belief in god(s) are atheists.
People without hair are bald.
People without sight or hearing are blind and deaf.
People without jobs are unemployed.
So forth and so on...
You make my point. All those things can be said to be characteristics. "Bald" is a characteristic, but there's no opposing word like "haired". Even a person with a lot of hair on their head is not referred to as "hairy". Likewise with the characteristic of atheism. There's no need for a word which means "not an atheist". There're probably dozens of words which necessarily imply "not an atheist" but those words represent opposing characteristics. In the case of cisgender, the opposing characteristic does not exist.
There's a group of persons. Within the group is a subset of persons without hair on their head. They are named bald persons, the rest are just persons.
There's a group of persons. Within the group is a subset of persons who have a disorder which makes them steal. They are called kleptomaniacs, the rest are just persons.
We don't need a new Latin-derived word to name persons who are not kleptomaniacs. And there are elephants and zebras, they have words. We don't a word need to specifically identify an elephant as a "not-a-zebra".
I don't know if you saw the other thread where we were beginning to touch on some mind/body philosophy when The Cadet suggested there is an "alignment" of the body and mind (someone else used a "switch" metaphor). I deny this because, as other persons have noted, the some persons have the characteristic of feeling a certain way, and the rest of us do not, so they are wanting to identify a non-thing.
I'd also add that part of my objection is that, like most Leftist ideas, it's ineffectual and/or counterproductive. If there is some negative stigma attached to having this disorder, changing my name (or theirs) will make no difference. Shakespeare wrote "What's in a name?". If ISIS changes their name to the Rainbows And Puppies Party, I'm not going to start thinking "y'know, genocide's not so bad after all". And it's counterproductive simply because people will dislike the attempt to further divide humanity and create more "us vs. them" which can result in people threatening people with death by baseball bat as in the pic posted earlier.