קביעת מין ומיניות

According to Jewish law, the legal gender of a person is determined by his or her external genitalia. Therefore, according to the halakha a person with testicular feminization or Swyer’s syndrome (XY gonadal dysgenesis) is considered to be female.

Despite her chromosomal profile, a woman with Swyer’s syndrome can become pregnant and give birth through ovum donation, IVF and embryo transfer to the womb after appropriate endocrinological preparation/pre-treatment.

(Note: I did not understand your question about a person with Klinefelter’s syndrome as he has a Y chromosome in addition to male genitalia.)