I assume that "transgenderism" can refer to a variety of phenomena from cross-dressing to expressing one's sexuality in a "non-binary" or "abnormal" fashion. Especially, it can refer to same-sex attraction based on gender dysphoria, which would be thought of as homosexuality or "unnatural lust" in ancient times. Before moving to the Church Fathers let's look at the New Testament writers.
The earliest opinions seem come from the letters of Paul.
Here, Paul addresses the issue of dressing inappropriately to one's sex:
Every man who prays or prophesies with his head covered dishonors his head, but
every wife who prays or prophesies with her head uncovered dishonors
her head, since it is the same as if her head were shaven... Judge for
yourselves: is it proper for a wife to pray to God with her head
uncovered? Does not nature itself teach you that if a man wears long
hair it is a disgrace for him, but if a woman has long hair, it is her
glory? For her hair is given to her for a covering. (1. Cor 11:3-15)
Thus, Paul assigns definite gender roles based on clothing, and by implication opposes cross-dressing or even the unintentional appearance of it. On the other hand, he would not have felt the need to write this to the Corinthian church unless others in the church practiced otherwise. We cannot say for certain that Paul's attitude here represented that of the early church.
Paul is even harsher in his condemnation of women and men experiencing what he called 'unnatural lusts' such as would be the case with transgender women feeling same-sex attraction because they are a man trapped in a woman's body, or vice versa.
God gave them over to shameful lusts. Even their
women exchanged natural sexual relations for unnatural ones. 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.
(Rom. 1 26-32)
The Letter of Jude likewise condemns abnormal sexuality. It apparently has homosexuality in mind, but since homosexual and lesbian acts can be expressions of transgenderism, this scripture should also be included:
Sodom and Gomorrah and the surrounding towns gave themselves up to
sexual immorality and perversion. They serve as an example of those
who suffer the punishment of eternal fire. (Jude 1:7)
Early Church Fathers
Among the Church Fathers, a notable passage is found in Justin Martyr, who bemoaned the birth of numerous hermaphrodites and also spoke of a type of sex-change operation, which he denounced as a "mutilation."
For this pollution [prostitution] a multitude of females and
hermaphrodites, and those who commit unmentionable iniquities, are
found in every nation. . .
And there are some who prostitute even their own children and wives,
and some are openly mutilated for the purpose of sodomy; and they
refer these mysteries to the mother of the gods” (First Apology 27
The Didache declared: “You shall not commit murder, you shall not commit adultery, you shall not commit pederasty (Didache 2:2).
The Exhortation to the Greeks, attributed to Clement of Alexandra, blesses a Scythian king mentioned by Herodotus because the king killed one of his citizens who:
having been deprived of his own virility in Greece, was now
communicating the effeminate disease to his fellow Scythians.
Tertullian denounced all kinds of non-marital and non-binary sexual behaviors:
Whoever enjoys any other than nuptial intercourse, in whatever place,
and in the person of whatever woman, makes himself guilty of adultery
and fornication... But all the other frenzies of passions — impious
both toward the bodies and toward the sexes — beyond the laws of
nature, we banish not only from the threshold, but from all shelter of
the Church, because they are not sins, but monstrosities. (On Modesty ch. 4)
Finally, Cyprian of Carthage denounces men who tend toward effeminacy to the point that the man (whether literally or not) "becomes a woman":
Men are emasculated, and all the pride and vigor of their sex is
effeminated in the disgrace of their enervated body; and he is more
pleasing there who has most completely broken down the man into the
woman. He grows into praise by virtue of his crime; and the more he is
degraded, the more skillful he is considered to be. Such a one is
looked upon—oh shame!—and looked upon with pleasure. . . (Letters 1:8
The online article What the Early Church Believed: Homosexuality presents a more complete survey of the Church Fathers' attitudes toward homosexuality and transgenderism.
Regarding the question about whether the Fathers interpreted the cited verses differently from "us," this depend on which modern readers are referred to in the OP. None of the Church Fathers or NT writers overtly approved of transgenderism and to the extent that they addressed the practice, they denounced it. However this does not mean they would take the view that certain types of transgenderism [especially natural hermaphroditism] should be excluded from the Church. Tertullian may be an exception. In addition Paul himself wrote that "in Christ there is no male or female." This saying may be used by inclusivist Christians today to support the view that transgenderism should be welcomed unconditionally in the church, but it hardly represents any known attitude of the NT writers or Church Fathers.