The Bible does not say anything about the origins of sexual orientation or whether it can be changed.

Some people believe that homosexuality is a choice people make and they could just as well choose to be heterosexual. However, The American Psychological Association says this about the origins of sexual orientation:

There is no consensus among scientists about the exact reasons that an individual develops a heterosexual, bisexual, gay, or lesbian orientation. Although much research has examined the possible genetic, hormonal, developmental, social, and cultural influences on sexual orientation, no findings have emerged that permit scientists to conclude that sexual orientation is determined by any particular factor or factors. Many think that nature and nurture both play complex roles; most people experience little or no sense of choice about their sexual orientation.11

Some groups claim to be able to change sexual orientation using “reparative therapy” or “conversion therapy.” However, studies claiming to show the effectiveness of these methods have been criticized as flawed and one widely quoted study has been retracted by its author.12

According to the American Psychological Association:

To date, there has been no scientifically adequate research to show that therapy aimed at changing sexual orientation (sometimes called reparative or conversion therapy) is safe or effective.11

The American Psychiatric Association states:

The validity, efficacy and ethics of clinical attempts to change an individual’s sexual orientation have been challenged. To date, there are no scientifically rigorous outcome studies to determine either the actual efficacy or harm of “reparative” treatments.13

Regarding therapy for gay and lesbian teens, the American Academy of Pediatrics states:

Therapy directed specifically at changing sexual orientation is contraindicated, since it can provoke guilt and anxiety while having little or no potential for achieving changes in orientation.14

Church Doctrine

Here is a sampling of official church positions on homosexuality from several large denominations in the United States:

Roman Catholic:

Basing itself on Sacred Scripture, which presents homosexual acts as acts of grave depravity, tradition has always declared that “homosexual acts are intrinsically disordered. They are contrary to the natural law. They close the sexual act to the gift of life. They do not proceed from a genuine affective and sexual complementarity. Under no circumstances can they be approved.

The number of men and women who have deep-seated homosexual tendencies is not negligible. This inclination, which is objectively disordered, constitutes for most of them a trial. They must be accepted with respect, compassion, and sensitivity. Every sign of unjust discrimination in their regard should be avoided. These persons are called to fulfill God’s will in their lives and, if they are Christians, to unite to the sacrifice of the Lord’s Cross the difficulties they may encounter from their condition.

Homosexual persons are called to chastity. By the virtues of self-mastery that teach them inner freedom, at times by the support of disinterested friendship, by prayer and sacramental grace, they can and should gradually and resolutely approach Christian perfection.
From Catechism of the Catholic Church, (c) 1994, United States Catholic Conference, Inc., http://www.nccbuscc.org/catechism/text/index.htm

Southern Baptist:

We affirm God’s plan for marriage and sexual intimacy – one man, and one woman, for life. Homosexuality is not a “valid alternative lifestyle.” The Bible condemns it as sin. It is not, however, unforgivable sin. The same redemption available to all sinners is available to homosexuals. They, too, may become new creations in Christ.
From Position Statements, Copyright (c) 1999 – 2001, Executive Committee of the Southern Baptist Convention, http://sbc.net/default.asp?url=position-statements.html

United Methodist:

Homosexual persons no less than heterosexual persons are individuals of sacred worth. All persons need the ministry and guidance of the church in their struggles for human fulfillment, as well as the spiritual and emotional care of a fellowship that enables reconciling relationships with God, with others, and with self. Although we do not condone the practice of homosexuality and consider this practice incompatible with Christian teaching, we affirm that God’s grace is available to all. We implore families and churches not to reject or condemn their lesbian and gay members and friends. We commit ourselves to be in ministry for and with all persons.

Certain basic human rights and civil liberties are due all persons. We are committed to supporting those rights and liberties for homosexual persons. We see a clear issue of simple justice in protecting their rightful claims where they have shared material resources, pensions, guardian relationships, mutual powers of attorney, and other such lawful claims typically attendant to contractual relationships that involve shared contributions, responsibilities, and liabilities, and equal protection before the law. Moreover, we support efforts to stop violence and other forms of coercion against gays and lesbians. We also commit ourselves to social witness against the coercion and marginalization of former homosexuals.
From The Book of Discipline of The United Methodist Church–2000, ¶161G, 162H. Copyright 2000 by The United Methodist Publishing House, http://www.umc.org/abouttheumc/policy/

Episcopal:

In 1976, the General Convention of the Episcopal Church declared that “homosexual persons are children of God who have a full and equal claim with all other persons upon the love, acceptance, and pastoral concern and care of the Church” (http://www.episcopalarchives.org/cgi-bin/acts/acts_resolution.pl?resolution=1976-A069″1976-A069). Since then, faithful Episcopalians have been working toward a greater understanding and radical inclusion of all of God’s children.

Along the way, The Episcopal Church has garnered a lot of attention, but with the help of organizations such as Integrity USA, the church has continued its work toward full inclusion of lesbian, gay, bisexual, and transgender (LGBT) Episcopalians. In 2003, the first openly gay bishop was consecrated; in 2009, General Convention resolved that God’s call is open to all; and in 2012, a provisional rite of blessing for same-gender relationships was authorized, and discrimination against transgender persons in the ordination process was officially prohibited.

To our lesbian, gay, bisexual, and transgender brothers and sisters: “The Episcopal Church welcomes you!”
From http://www.episcopalchurch.org/page/lgbt-church

The Episcopal Church now permits same-sex marriages and language relating to marriage has been changed from “a man and a woman” to “two persons” to reflect the change:

Rite for holy matrimony in the Episcopal Church (BCP, p. 423). Marriage is a solemn public covenant between two persons in the presence of God. At least one of the couple must be a baptized Christian. Prior to the marriage, the couple sign a declaration of intention. It states that they hold marriage to be a lifelong union; that they believe this union in heart, body, and mind is intended by God for their mutual joy, for help and comfort given one another in prosperity and adversity, and for the procreation (when it is God’s will) of children and their Christian nurture. There must be at least two witnesses for the ceremony. A priest or bishop normally presides at the marriage. If no priest or bishop is available, a deacon can preside if permitted by civil law. A deacon presiding at the marriage would omit the nuptial blessing. The marriage may be celebrated and blessed in the context of a nuptial eucharist. The marriage service then replaces the ministry of the word, and the eucharist begins with the offertory. Any authorized liturgy for the eucharist may be used with the marriage service. Prior to the service, the Banns of Marriage may be posted to announce the upcoming marriage and insure that there is no impediment.
From: http://www.episcopalchurch.org/library/glossary/celebration-and-blessing-marriage