Does the Christian church have an official position on Beauty?

Yes. From the High Middle Ages, the Catholic Church teaches that we can recognize the three transcendentals of Truth, Beauty, and Goodness as

... objective features of everything that exists, they are in a sense attributes of God.

As God has revealed Himself and Hs creation to us over time we have come to recognize three transcendentals, Truth, Beauty, and Goodness. These transcendentals, as properties of being, can teach us about God.

(Source: Beauty is Transcendent)

Catholic Catechism CCC 2500-2503 discuss applying Truth, Beauty, and Sacred Art in the context of obeying the eighth commandment ("You shall not bear false witness against your neighbor") which is part of the second great commandment "You shall love your neighbor as yourself":

2500 The practice of goodness is accompanied by spontaneous spiritual joy and moral beauty. Likewise, truth carries with it the joy and splendor of spiritual beauty. Truth is beautiful in itself. Truth in words, the rational expression of the knowledge of created and uncreated reality, is necessary to man, who is endowed with intellect. But truth can also find other complementary forms of human expression, above all when it is a matter of evoking what is beyond words: the depths of the human heart, the exaltations of the soul, the mystery of God. Even before revealing himself to man in words of truth, God reveals himself to him through the universal language of creation, the work of his Word, of his wisdom: the order and harmony of the cosmos-which both the child and the scientist discover-"from the greatness and beauty of created things comes a corresponding perception of their Creator," "for the author of beauty created them." (Wis 13:3,5)

2501 Created "in the image of God," (Gen 1:26) man also expresses the truth of his relationship with God the Creator by the beauty of his artistic works. Indeed, art is a distinctively human form of expression; beyond the search for the necessities of life which is common to all living creatures, art is a freely given superabundance of the human being's inner riches. Arising from talent given by the Creator and from man's own effort, art is a form of practical wisdom, uniting knowledge and skill (Wis 7:16-17), to give form to the truth of reality in a language accessible to sight or hearing. To the extent that it is inspired by truth and love of beings, art bears a certain likeness to God's activity in what he has created. Like any other human activity, art is not an absolute end in itself, but is ordered to and ennobled by the ultimate end of man (cf. Pius XII, Musicae sacrae disciplina; Discourses of September 3 and December 25, 1950).

2502 Sacred art is true and beautiful when its form corresponds to its particular vocation: evoking and glorifying, in faith and adoration, the transcendent mystery of God - the surpassing invisible beauty of truth and love visible in Christ, who "reflects the glory of God and bears the very stamp of his nature," in whom "the whole fullness of deity dwells bodily." (Heb 1:3; Col 2:9) This spiritual beauty of God is reflected in the most holy Virgin Mother of God, the angels, and saints. Genuine sacred art draws man to adoration, to prayer, and to the love of God, Creator and Savior, the Holy One and Sanctifier.

2503 For this reason bishops, personally or through delegates, should see to the promotion of sacred art, old and new, in all its forms and, with the same religious care, remove from the liturgy and from places of worship everything which is not in conformity with the truth of faith and the authentic beauty of sacred art. (cf. SC 122-127)

Answering your questions

Question:

How are we to understand our own aversion to individual parts of divine creation?

Answer: St. Augustine understands evil as corruption/absence of the good in a particular being within creation. We can then conceive our aversion to ugliness as recognizing the cloud over potential beauty that a human being, part of nature, or an object of art could have had by participating more fully in God's Beauty. Thus, our aversion has to do with the sadness / horror / tragedy of the missing/corrupted element in a being, such as a handicapped person, an ugly musical performance, a broken sculpture, the fallen worship angel Lucifer, etc. which we may trace further to either unredeemed creation or to sin.

Question:

Accepting that this is a common human experience, is there a moral Christian imperative to cultivate beauty, as an aid to faith in God?

Answer: Yes, there are several ways:

1. by transforming our perception and enjoyment of beauty in nature into thanksgiving to our creator God
2. by being mindful when creating/enjoying human works of art that we participate in God's creativity and draw inspiration from God as the source of all objective beauty
3. by realizing that the very faculty of our soul that recognizes beauty comes ultimately from God who possesses it to the fullness, and we strive to cultivate this faculty further
4. by expressing beauty to others as a complement of truth and goodness (see CCC 2500-2503 above).

Question:

I suppose it risks shading over into a sort of Nietzschean worship of the superman, or simply into idolatry.

Answer: It would become idolatry ONLY IF the practice of beauty is divorced from the source of objective beauty (the transcendent creator Christian God of the Bible) by making the work of art an end in itself which can degenerate into subjective beauty characteristics of so many modern art.