The Bible reference in Ezekiel is a prophecy about the Latter Days. Many Christian Groups still practice the wearing of holy vestments from Biblical times. Eastern Orthodox Christians being a good example who trhough tradition have kept the form from the early Apostolic times.
There is a rich history in Christianity on the use of the garment. There are many historical Christian examples if you want to learn more about the Christian tradition of Holy Garments from the Biblical as well as post apostolic times. Just a google search away if you are really interested.
Of course many priests Catholic, Lutheran and even Born Again pastors have some form of Holy vestment. Our founding Father Geroge Washington and other founders as well.
What the real question should be is why some modern Christians have given up the centuries long practice of Christian Holy garb that was even practiced recently by our Founding Fathers?
>>If so, where does it say women will be required to wear them...Origen answers this in one of his sermons in the last paragraph below. (though the earlier paragraphs are instructive as well) [ie God gave the garment to Adam and the woman Eve and the later Christian garment is symbolic of that.]
The Linen Garment
Clement's letter to Theodore also sheds some light on the early Christian mysteries. In this document, Clement wrote to a certain local church leader who had asked several questions about a document called the Secret Gospel of Mark, which a libertine Gnostic group called the Carpocratians had corrupted to suit their agenda. Clement decried the fact that the Gnostics had corrupted the text and described the document as an expansion of Mark's canonical gospel written after Peter died:
[Thus] he composed a more spiritual Gospel for the use of those who were being perfected. Nevertheless, he yet did not divulge the things not to be uttered, nor did he write down the hierophantic teaching of the Lord, but to the stories already written he added yet others and, moreover, brought in certain sayings of which he knew the interpretation would, as a mystagogue [teacher of mysteries], lead the hearers into the innermost sanctuary of that truth hidden by seven [veils]. Thus, in sum, he prearranged matters, neither grudgingly nor incautiously, in my opinion, and, dying, he left his composition to the church in Alexandria, where it even yet is most carefully guarded, being read only to those who are being initiated into the great mysteries.63
Even though the fragments we have of the Secret Gospel of Mark do not reveal the secret teachings, it may give us one more detail about what Clement called "the great mysteries." Clement includes a passage from the Secret Gospel in his letter which tells of Jesus teaching the mysteries to a young man whom he had recently raised from the dead:
And after six days Jesus told him what to do and in the evening the youth comes to him, wearing a linen cloth over [his] naked [body]. And he remained with him that night, for Jesus taught him the mystery of the Kingdom of God.64
Therefore, it may be inferred that people participating in the "great mysteries" were dressed in linen robes.65 Certainly it would have been standard procedure to call for special ritual clothing in such an important rite, just as was done for the rites of the temple at Jerusalem. And indeed, references to special symbolic garments or robes abound in early Christian literature. Note, for example, that the Shepherd of Hermas includes a description "of a marked secret and symbolic nature" of twelve virgins clothed in white linen. The angel told Hermas that nobody can enter the Kingdom of God unless he is clothed in their garments.66
Origen insisted, in a sermon on the book of Leviticus, that the faithful must have garments kept apart from the common clothing of the world:
Therefore, you have a priesthood because you are 'a priestly nation,' and for this reason 'you ought to offer an offering of praise to God,' an offering of prayers, an offering of mercy, an offering of purity, an offering of justice, an offering of holiness. But in order to offer these things worthily, you must have clean clothes separated from the common clothing of the rest of humanity . . . .67
In these sermons Origen compared the Christian garment (whether it was real or figurative) to the garments given to the Temple priests, and likened these to the skin tunics given to Adam and Eve by God:
But before we begin to say something about this kind of garment, I want to compare those miserable garments, with which the first man was clothed after he had sinned, with these holy and faithful garments. Indeed, it is said that God made those. "For God made skin tunics and clothed Adam and his wife." Therefore, those were tunics of skins taken from animals. For with such as these, it was necessary for the sinner to be dressed. It says, "with skin tunics," which are a symbol of the mortality which he received because of his skin and of his frailty which came from the corruption of the flesh. But if you have been already washed from these and purified through the Law of God, then Moses will dress you with a garment of incorruptibility so that "your shame may never appear" and "that this mortality may be absorbed by life."68