What's being objected to, is the idea that people are morally required to pursue the extinction of same-sex attraction feelings, and the dominance of heterosexual feelings. Feelings can neither be bidden nor banished. It's how you react to feelings, which can be changed.
Leaders (or those who used to be leaders) in the major ex-gay and orientation-change organizations are more and more saying that what is needed is not the development of a heterosexual appetite, but the development of discipleship no matter what your appetite may be. The goal is to learn to live gracefully and chastely whether you think you're "gay" or "straight" or whatever your (usually unhelpful) appetitive label may be.
At least, that's my understanding of it.
Heterosexual Christian Singles are not supposed to give in to their lustful sexual desires. Homosexuals, some who may be Christians, likewise are not supposed to act upon their lustful sexual desires. It’s really that simple. Control your actions. Don’t give in to your lustful sexual feelings, whether heterosexual or homosexual.