This is an important question which can only be answered on a clear foundation. For Orthodox Christians, the authority is (1) the words of Jesus Christ (2) the apostolic teaching (3) the consistent testimony of the ancient Fathers. In the case of homosexuality, there are also anthropological reasons which simply confirm the above.
The main point of reference here is the words of Jesus in Matthew 10:5-8; “But Jesus said to them, “For your hardness of heart he wrote you this commandment. 6 But from the beginning of creation, `God made them male and female.’ 7 `For this reason a man shall leave his father and mother and be joined to his wife, 8 and the two shall become one flesh.’ So they are no longer two but one flesh.”
This sets the divinely appointed parameters for unity and complementarity between human beings. In homosexual relations, one party actually takes on the role of the opposite sex in order to pretend that such complementarity exists. As a result, it might be said that homosexuality does not truly exist or function.
In addition to this, Jesus condemned “porneia” (Mark 7:21; Matthew 15:19), a term which included any form of sexual immorality, including homosexuality. This is confirmed by Jude 5-8 and by St. Paul’s very specific language in 1 Corinthians 6:9.
It should be reminded that homosexuality was very commonplace in the Greek world, and the Christian rejection of homosexual practice (which is different than inclination) as a grave sin is consistent with the entirety of Revelation.
The Church is therefore a place of healing and regeneration which sees sinful inclinations and practices for what they are, in the Holy Spirit. Homosexuality is one of them, not one that should be singled out while many others “dishonesty, greed, substance abuse, violence, etc” (1 Corinthians 6:10; Galatians 5:20-21) are ignored.