They are not far away, because they both lie in Love and this Universe will not exist without it. Yes, it is possible to stay pure and holy and many of our Christian Saints have done this. St Theresa of Avila; St. John of the Cross; St. Augustine; Theresa of Lieusieux; Meister Eckhart; Julian of Norwich, to name a few.
Purity is the Light of the soul expressing itself in and through the physical; the inner vessel that holds the Light. A holy or sacred life itself involves purity and this exists, like a ladder with many rungs. It has several levels. Cleanliness and modesty as well as sweetness in speech, thought and actions are a large part of it.
If we say it is impossible, then we are really negating the gifts of prayer and the words of our Lord who says 'Blessed are the pure...'
Purity manifest through holiness, a life of humility, kindness and magnanimity and other inner virtues, none of which can happen without spiritual practice.
"Purity is the light of our soul expressing its divinity through the body, the vital and the mind.... Purity is the Breath of the Supreme. When purity leaves us, the Breath of the Supreme also leaves. Then we are left with only our human breath." -Sri Chinmoy.
Purity is the life-breath of God and apart from Gratitude, it is one of the most significant virtues. Our Christianity calls it the lily of all virtues and a pure Heart is like that of a child's - a peerless manifestation of God's Divine Reality.
Purity must be established in the entire existence of body and soul and is integral and essential to spiritual practices. Nevertheless, in the process of evolution it takes time to develop and is a very slow process. Purity is cleanliness of thoughts, words and actions, evn in the state of dreams. True holiness is accompanied by a purity-life.
" Purity means following the dictates of our Inner Pilot without allowing undivine forces to enter into us. Wherever there is a lack of purity there is obscurity, which is the pioneer of death. What we call obscurity today is death for us tomorrow. Purity is the only thing that can sustain our divinity. If there is no purity, there is no certainty. If there is no purity, there is no spontaneity. If there is no purity, there is no constant flow of divinity inside us." -Sri Chinmoy