Whether you view sexuality as a choice or an inherent quality is very important to this issue. People will firmly stand on their belief (and without conclusive evidence it can only be a belief) that a person is inherently “orientated” a specific way and cannot and should not try to change it. The person has no responsibility for it because they are deemed not to be in control of it. The problem in that belief is that if you believe you have no control over something you tend not to waste your time or energy trying to change it.
My sexuality is a choice. I choose to be heterosexual every day and that is an easy decision for me. I never really entertained homosexual desires; as a result that's not really an issue for me. I also choose to be faithful to my wife every day - in thought, word, and deed. This is much more difficult for me because many past years of entertaining wrong heterosexual desires (which were as harmful to me at the time as homosexual ones would have been) was actually encouraged by the society I grew up in. I choose daily with God’s help to make my desire for my wife alone and to the exclusion of all others. I choose not to entertain desires that are contrary to the covenant I have made with my wife and when I fail it is God who helps me to return and reassert my commitment to our covenant (Matthew 5:28 and 15:19).
People get so caught up in making their emotions the definer of their identity but emotions are fleeting and unreliable. Desires and emotions are good servants but poor masters (Jeremiah 17:9).