Please note I’m typing this as a trans man. Being “cis” or “trans” stems from someone’s gender.

Basically, do you identify as your birth gender (not sex, gender and sex are different)? If the answer is yes, you are “cis”. If the answer is no, like I my case, I was born female, I identify as a male, then you are are trans.

I hope this answers your question.

I understand what they are, I'm asking if there is a name for the category of characteristic that they both belong to.

I'm not entirely sure there is a word for it. If not, maybe there should be.

I understand what they are, I'm asking if there is a name for the category of characteristic that they both belong to.

You're not getting an answer to your question because the question, as stated, is incomprehensible. You're asking for a "category of characteristic" that a pair of antonym adjectives "belong to"? That doesn't make sense. They apply to a whole host of characteristics, because they're not describing a specific characteristic, but how a characteristic relates to the whole. Just like "homo" and "hetero"; homozygous, heterogenous, homocystine, and heterophony are all words that use the "homo" or "hetero" prefix to describe how those words relate to other concepts in their category. It's the same with "cis" and "trans". The prefixes don't "belong" to a category of characteristics, they explicitly exist outside of the characteristics of the words their modifying.

That's the best I can do with the way you've chosen to phrase your question, and I admit it's a reach, but your question is gibberish.

Male, female or nonbinary are a person's gender.
White, black, asian (nonexclusively) are a person's race.
Right, left are a person's handedness.
Cis, trans are a person's ________.

Gender identity.