I do not believe the chromosomes give us the whole being transgender, but its based off of the whole of the hormones that would be thus creating it.
I mean basis under generic genetics the whole xx or xy sex chromosome match is not really the cause of female/male determination, but there is a specific gene that is "usually" on the y chromosome, which is the "SR Y" gene. This gene is basically the determination of the outward appearance of male and/or basis thereof more testosterone hormones to be in the body.
There is also the fact of Turner Syndrome being simply x_ where there is of course the missing chromosome match, which of course would cause changes to the growing baby from womb as well as through life. Then there is a slew of Klinefelter's Syndrome represented as xxx, xxy, xyy, xxxx, xxxy, xxyy. These chromosome matches do happen, humans with these matches do get features that would be of both of the binary sexes, and or other differences to the body. Does this make anyone transgender? The answer is still a no, though it does have a chance that someone could be intersex, though not everyone with these matches.
Okay back to the whole "SR Y" gene. It generally does have a place on the small arm of the y chromosome, though through meiosis, there are possibilities it can then be transposed onto an x chromosome, or be removed from the y chromosome. These instances are pretty rare, but can happen nonetheless. I have also read an article quite some time back, I can't remember the exact date of when I read it, nor the article release date nor the headline, but it was about scientists that were able to medically transpose the SR Y gene to an xx chromosome match, or even removing it from the xy chromosome pair on mice and to see what would happen. I know it sounds bad being medical tests on animals and such, and since I cannot at this time find the article, it may seem a little farfetched. But without that article I would have never talked to my instructor for my genetics course, for hours on the subject purely on gender alone.
Anyways this is just a little food for thought. And clearly in statement even xx and xy chromosome matching does not give the final outcome of female, male, or transgender.
Kate <3