Typically, proponents of this view would say something like the attraction is an indication of sin that is already present. They do not believe the attraction is inherent within that person, but rather is the effect of other sins.
To support this they would often quote Romans 1.
18 The wrath of God is being revealed from heaven against all the godlessness and wickedness of people, who suppress the truth by their wickedness, 19 since what may be known about God is plain to them, because God has made it plain to them. ...
21 For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened. ...
24 Therefore God gave them over in the sinful desires of their hearts to sexual impurity for the degrading of their bodies with one another. ...
26 Because of this, God gave them over to shameful lusts. Even their women exchanged natural sexual relations for unnatural ones. 27 In the same way the men also abandoned natural relations with women and were inflamed with lust for one another. Men committed shameful acts with other men, and received in themselves the due penalty for their error.
28 Furthermore, just as they did not think it worthwhile to retain the knowledge of God, so God gave them over to a depraved mind, so that they do what ought not to be done. 29 They have become filled with every kind of wickedness, evil, greed and depravity. They are full of envy, murder, strife, deceit and malice. ... 32 Although they know God’s righteous decree that those who do such things deserve death, they not only continue to do these very things but also approve of those who practice them.
When challenged that same sex attraction is an issue of psychology, not theology, they would say that these verses clearly state the root of this psychological problem. It starts as a problem within their heart. They hate the laws of God and some even hate God Himself. They desired wickedness more than God's righteousness, so God gave them over to their wickedness. Not only would they like to engage in homosexual acts, but they now have a mind that is intrinsically attracted to that sin. Conversely, opposite sex attraction is blessed and holy and is properly sought within marriage. No such thing exists for homosexuality.
Most taking this view would likely not call it a sin, per se, but it is the fruit of sin that has been prevalent since the beginning. As an imperfect analogy, many would agree that theft is a sin, but some would also say that using that stolen item is continued theft.
I'm still looking for other corroborating sources, but they are hard to come by. It is not a popular opinion and many who do hold it are usually pretty hateful about it.
St. Thomas Aquinas has an illuminating view on Romans 1:24
Wherefore, God gave them up to the desires of their heart [because they "worshiped and served the creature rather than the Creator" (v. 25)], unto uncleanness: to dishonor their own bodies among themselves
Cap. 1 l. 7 discusses the causality of homosexuality:
139. But since impurity of this kind is a sin, it seems that God would not give men over to it: God himself tempts no one to evil (Jas 1:13).
The answer is that God does not give men over to impurity directly, as though inclining a man's affection toward evil, because God ordains all things to himself: the Lord has made everything for himself (Prov 16:4), whereas something is sinful through its turning from him. But he gives men over to sin indirectly, inasmuch as he justly withdraws the grace through which men are kept from sinning, just as a person would be said to cause another to fall, if he removed the ladder supporting him. In this way, one's first sin is a cause of the next, which is at the same time a punishment for the first one.
To understand this it should be noted that one sin can be the cause of another directly or indirectly: directly, inasmuch as from one sin he is inclined to another in any of three ways. In one way, when it acts as a final cause; for example, when someone from greed or envy is incited to commit murder. Second, when it acts as a material cause, as gluttony leads to lust by administering the material. Third, when it acts as a moving cause, as when many repetitions of the same sin produce a habit inclining a person to repeat the sin.
Indirectly, when the first sin merits the exclusion of grace, so that once it is removed, a man falls into another sin. In this way the first sin is the cause of the second indirectly or incidentally, inasmuch as it removes the preventative.
(translation from: Larcher, Fabian R., trans. Commentary on the Letter of Saint Paul to the Romans, ed. John Mortensen and Enrique Alarcón, with parallel Latin and the Greek text of the epistle. Lander, Wyo.: The Aquinas Institute for the Study of Sacred Doctrine, 2012. pp. 47-8)
In other words: He, the Author of nature, does not put same-sex attraction in human nature.
Aquinas is saying that "one's first sin" "is a cause of the next". Relative to this topic, the homosexuals' personal sins (idolatry, spite for God, etc.) made them even greater sinners (not just doers of homosexual acts, but those who long for that evil).