I think we generate contexts all the time...but in this instance I'd say the creation of context (as opposed to a recognition of fact regardless of what we do with the fact) is mostly on the side of those who came up with the notion of gender identity, as if gender was a subjective value, something we decide upon, and not an operation of biology. We are born to a sex. Within the parameters of that sex we've constructed all sorts of contextual social niceties and expectations. A lot of that is pure invention. We aren't obliged to conform. We consent to it.
To say to yourself, "I think I'm a woman. I will conform my physical reality, to the extent possible, to that belief," is to mutilate yourself not out of necessity, but because you've first accepted the subjective context that defines what your sex must be and how it must function.
Which to my mind would indicate just how powerful and overwhelming self-image is, relative to biological form.
The question then becomes: are these biologically contradictory self-images something that the rest of us should abide, or are they something we should be trying to "correct" in some way? As an example, if someone believed they were a dog, even though they are biologically a human, we would consider this an anomaly that needs to be "corrected", if possible. Not something that human society should be trying to accommodate. Yet humans born with male genitalia who believe they are women is being proposed as an anomaly that human society should be trying to accommodate. And the question is why? How is this anomaly determined to be reasonable enough to accommodate, while other similar self-image anomalies would not be?
Granted, my analogy is extremely disparate in terms of numbers of humans representing such anomalies. (Is there a human, anywhere, who actually believes they are a dog? I doubt it.) But it serves as a way of illuminating the actual logical question regarding such social accommodation of irrational self-image.
My own feeling is that because there are examples of such gender contradictory self-image in every culture in every time throughout history, that there is more than just a psychological cause. I believe there is also a biological component involved. Which does separate these anomalies from those that are purely psychological and therefor considered "insane".
I also feel that there is little actual danger involved for someone with a gender contradictory self-image compared to the danger involved for other psychological self-image anomalies (with the exception of self-mutilation, which does not seem a significant issue).
So I'm inclined to see no reason why society should not accommodate these particular anomalies. As I believe it's healthy for us as a whole to practice at accommodating those who are more rare and unusual, among us. Variety is always better than conformity in large groups, and adaptability is a very important characteristic for any society to practice and maintain.