In summary: if a person touches his penis, it is recommended for him to perform ablution in all cases, whether with desire or without desire. If he touches it with desire, the view that ablution is obligatory is very strong, though I cannot state it conclusively. As a precaution, he should perform ablution.
Touching both of the genital organs of an indeterminate intersex person, and a male touching its penis or a female touching its vulva with desire in either case . . .
His statement, “touching both of them of an indeterminate intersex person”: “both of them” refers to the vulva and the penis. “An indeterminate intersex person” is one whose sex is not known—whether male or female.
That is, if one touches both the vulva and the penis of an intersex person, his ablution is invalidated, because he has touched an actual genital organ, since one of the two is certainly an actual genital organ.
His statement, “and a male touching its penis,” means a male touching the penis of the intersex person with desire.
His statement, “or a female touching its vulva,” means a female touching the vulva of the intersex person with desire.
His statement, “with desire in either case,” means when a male touches the penis of the intersex person, or a female touches its vulva.
For example, there is an intersex man and a man who is not intersex. The latter touches the penis of the intersex person with desire, and thus his ablution is invalidated . . .
The reason is that, when he touches this part of the person’s body with desire, then if the person is female, he has touched her with desire; and touching a woman with desire invalidates ablution according to the madhhab, as will come (1). If the person is male, then he has touched his penis, and touching a penis