The passage is not praising Mary's private parts; it is praising her complete sexual purity and explaining the miraculous conception of Jesus. The word farj can refer to the private part, but it also functions as a modest idiom for chastity, and the grammar does not create the contradiction alleged.
What the objection is really saying
The strongest form of the objection is understandable: Mary is one of the most revered women in the Quran, yet the text says that she guarded her farj, a word that can denote the sexual organ. The critic argues that publicly directing attention to a woman's genitals is an indecent way to honor her. He also points to apparently varying masculine and feminine forms in the descriptions of Mary, especially in Quran 21:91, and sees this as evidence of awkward or inconsistent wording.
That criticism should not be answered by pretending that farj has no bodily meaning. It can have that meaning. The question is how the word is being used and what the passage is actually praising.
What the verses actually say
"And Mary, daughter of Imran, who guarded her chastity, so We breathed into it of Our spirit; and she confirmed the words of her Lord and His Scriptures, and was among the devoutly obedient."
Quran 66:12
The central praise is that Mary guarded herself from sexual violation and immorality. This is why many translations reasonably render farjaha as "her chastity" or "her virginity." The Quran uses the same idiom elsewhere when it commands believing men and women to "guard their private parts" (Quran 23:5; 24:30-31). That is not erotic language. It is moral language about sexual integrity.
Nor is the verse saying that God physically entered a sexual organ. In Quranic usage, "Our spirit" refers to a created spirit specially honored by its attribution to God, and the classical commentators explain the conception as occurring through the action of the angel Gabriel, by God's command. The pronoun in "into it" has been discussed by exegetes, with explanations referring to Mary, her womb, or the opening of her garment. None requires a crude or literalistic image of God.
The grammar is not inconsistent
"And Mary, who guarded her chastity, so We breathed into her of Our spirit and made her and her son a sign for all worlds."
Quran 21:91
The feminine forms - allati, "who," and ahsanat, "she guarded" - agree with Mary. The noun farj is grammatically masculine in Arabic, while the attached suffix -ha is feminine because it means "her." This is normal Arabic grammar, not a claim that Mary is masculine. In 21:91, fiha, "into her," is feminine because the pronoun refers to Mary or another feminine referent in context. Different pronouns can occur because their antecedents are understood differently; this is not a grammatical contradiction.
The wording therefore establishes Mary's chastity and the miraculous nature of Jesus' birth. It does not establish that the Quran speaks indecently, that it sexualizes Mary, or that its grammar is confused. A bodily term used as a restrained moral euphemism is not, by itself, vulgar language.