Within the general population, it is well established that not all individuals conform to XY or XX. There are a number of variations, the true proportion of those variations is unknown because very few of us have our DNA analyzed.
Karyotype does not define sex.
I do think that as far as functioning in society, it is more important whether one feels themselves to be male, female, neither male or female or both male or female than what external or internal sex organs are present. Medically, there are different implications depending on what sex organs are present, both externally and internally.
Whether a person "feels themselves to be" male or female shouldn't have any bearing on whether or not they get to strip down in front of the opposite sex. Medically, yes, the presence of certain organs drives a lot of treatment. But as for society at large, I do NOT think that a person's subjective feelings is more important than their objective reality.
If we were to take your statement as fact, then the result is that if a male person with an entirely male body thinks of themselves as a woman... then because of what they claim to feel, they get placed into female prisons with female inmates. They get to strip down and use the female side of the Korean Spa, because their internal feelings are more important than the objective fact that they're a male who is showing off their male genitals to a bunch of women without their consent. Your position argues that if a person merely says that they feel like a women, then they can demand to be housed in a female-only rape shelter, play in female athletic sports, and provide intimate care to female patients who have requested a female carer.
I personally believe that rigid norms as to what is considered male and what is considered female behavior or what are considered male or female attributes is artificially constructed and is damaging.
I agree that rigid norms regarding
behavior are damaging.
On the other hand, our bodies aren't artificial constructs, nor is the abuse and discrimination that women have faced throughout the millennia as a result of our sexed bodies. Young women aren't having their clitorises removed and their vaginas sewn shut because their sex is an artificial construct, nor is it because they "feel like a girl" inside their brains. Infants aren't having their foreskin cut off because of an artificial construct, nor because of how they view their personalities with respect to gendered stereotypes. 98% of rape victims aren't being raped because of an artificial construct, nor are they raped because of how they feel on the inside.