There are new and old testament prohibitions against dressing like the opposite sex as well as engaging in same sex activity. Many christians love to point that out while forgetting to add that the bible prohibits all sexual immorality in both the new and old testaments so fornicators are not without guilt. Any sexual activity outside of a traditional man-woman marriage is prohibited.
I know people have natural fleshly desires and tendencies. There is no gay gene so I wouldn't really agree with "born this way". I can believe a tendency that one chooses to engage or not engage. In orthodoxy we call these fleshly desires and tendencies "passions". People are drawn to sex, money, drugs,fame, power, thrill seeking, etc. Every person will have their particular passions they will war against. The goal of an orthodox christian life is to rid oneself of the passions, to remove them from between you and the Lord, because they separate us from him. This is why we try to refrain from judging others. You need to worry about what's on your own plate and if one is honest with oneself that is enough to keep a person busy. To judge a person unworthy because they have engaged in sexual immorality is to place yourself in a judgement seat that belongs to Christ only and set your own self up as judge. A grave error. We can judge the deeds but not the person. The orthodox church is meant as a spiritual hospital where we are offered forgveness for our sins through confession and holy communion, not a courtroom where we condemn others. Thanks for asking!