This answer is highly based on Scriptural exegesis which evidently supports ultra-conservative traditional Christian doctrine on gender. In Biblical Hermeneutics, our goal is to interpret the Scripture in its own socio-religio-cultural context.
The Greek word μαλακος literally means "soft" (figuratively, "weaklings").
The Gospels had μαλακος referring to clothes. They are "soft clothes" (fine clothes) worn by rich people (Matthew 11:9, Luke 7:25).
μαλακος in 1 Corinthians 6:9 refers to people specifically males "behaving softly" (effeminate, womanly) by abusing themselves through being passive partner in homosexual sexual acts. This effeminate behaviour is condemned by Paul as sinful.
According to scholars, μαλακος refers to (i) effeminate boys and men (ii) passive in homosexual sexual acts, usually in the context of (iii) male prostitution, shrine prostitution, pederasty and effeminacy. These males actively chose to abuse themselves with other males sexually.
In classical Greek, μαλακός was also used to refer to boys and men who allowed themselves to be used homosexually.4 It was also applied to a man taking the female or passive role in homosexuality.
Dionysius of Halicarnassus, who wrote Roman Antiquities around 7 B.C., described Aristodemus of Cumae as μαλακός because he had been “effeminate” (θηλυδρίας) as a child and had undergone the things associated with women. 5 In classical literature the word μαλακός is sometimes applied to obviously gay persons. Lucian describes the blood of some priests he condemns for passive homosexual behavior as μαλακός.6 This cannot be dismissed as not indicating anything about the sexuality of the individuals in question. These were priests who spent their time seeking group sexual encounters. While there is some ambiguity with regard to μαλακός, it is not beyond reason to see the word representing the passive parties in homosexual intercourse. This is even more reasonable when it is in juxtaposition with ἀρσενοκοιτής which does imply an active homosexual role. It is interesting that in Aristotle’s Problems, a lengthy discussion of the origins of homosexual passivity, he employs the word μαλακός. In its general sense the word does mean “unrestrained,” but not without any particularly homosexual context.’, Ukleja, ‘The Bible and Homosexuality Part II: Homosexuality in the New Testament’, Bibliotheca Sacra.
The μαλακος as described above by scholars also refers to someone who is effeminate” (θηλυδρίας) as a child and had undergone the things associated with women.
Thus, it reasonable that μαλακος (effeminate) includes not only being passive homosexual sexual act but also being feminised by clothing (cf. Deuteronomy 22:5) and cosmetics. Based on Bible scholars, historically these were specifically the feminised eunuchs who were feminine even at a young age (Philo, Josephus).
This is what Josephus wrote about eunuchs: "Turn away from eunuchs and flee from those who have deprived themselves of their manhood and its fruit..."by reason of the effeminacy of their soul they have changed the sex of their body also"" (Ant 4.290-291). This says that eunuchs have feminine souls, and "desire to be completely changed into women" as Philo puts it and thus "rearrange the body" as Josephus says. So when Jesus talked about eunuchs, his disciples would have likely thought about transgender people. Josephus found eunuchs to be "monstrosities", that's the word he used, to be shunned like murderers.
Josephus was commenting on Deut 23:1-6 which excludes eunuchs from the assembly. Philo commented on the same passage in Spec. Leg. 1.325 saying that the Law excludes those "who belie their sex and are affected with effemination ... for it expels those whose sex organs are fractured or mutilated, who husband the flower of their youthful bloom...and restamp the masculine cast into a feminine form". Again this describes people who today would be regarded as trans.
Eunuchs are "those whose penis had been cut off and crushed their testicles" (Deuteronomy 23:1 NLT).Jesus Christ told us that eunuchs are not getting married (the reason is because their genitalia is deformed). (Matthew 19:12). Those "born eunuchs" refers to those born with birth defects related to their genitalia (it was like the genitalia of eunuchs made by man: it was deformed but only naturally since it had been since from the mother's womb, says Christ). Most probably it refers to some form of intersex condition where the person is born with ambiguous genitalia. Intersex should not marry according to Matthew 19:12:
Jesus’ saying about eunuchs in Matt 19:12 presupposes that eunuchs are not having sexual intercourse at all, let alone having forbidden sexual intercourse. (THE GOSPEL OF JESUS ON SEXUAL BINARIES, by Robert A. J. Gagnon)
If the born male eunuchs [intersex] in Matthew 19:12 feminised themselves, they will become μαλακος of 1 Cor 6:9 and thus, in this case the intersex is condemned. The right thing for born eunuchs to do is to live celibate lives and not change their original state.
Transgender women as we know it today shares some attributes of feminised eunuchs such as feminisation (i) by being passive in sex, (ii) by transvestitism, (iii) by cosmetics. The difference is that the goal of these modern day feminised males is to live as the opposite sex due to gender dysphoria, some even are asexual whilst the goal of the feminised males (i.e. μαλακος) in 1 Corinthians 6:9 is to seek male partners for sex (to abuse themselves with mankind, KJV). However, the Bible condemns any act of feminisation regardless of reason, even when the reason itself is not sinful (such as gender dysphoria, DSM-5, gender incongruence, ICD-11), because:
(i) people born with normal genitalia should only marry people of the opposite sex (Romans 1:26-27), and in fact, the Bible is so strict that
(ii) only people born with normal genitalia can marry (Matthew 19:12).
Thus, homosexuals, transgender and even intersex are not allowed to get married under this Biblical perspective. Applying this concept in modern science means that only the phenotypic sex (assigned sex at birth, whether normal or intersex), not genotypic sex (sex chromosomes), is the basis of true gender in the Bible. Thus, any act of changing one's phenotypic sex is prohibited such as those with ambiguously genitalia (intersex) and with gender dysphoria (transgender) (exception is for the person who made himself an eunuch to be celibate in Matthew 19).
Conclusion
Μαλακος in 1 Corinthians 6:9 refers to males (people born with male genitalia) who were:
(i) taking the outward form of females (by wearing female clothes and cosmetics to attract male sexual partners),
(ii) taking the sexual role of females (passive in sex, being sodomised by the αρσενοκιτες).
These males are literally living as the opposite sex. Scholars identified these males historically as the following:
(a) male prostitutes (in temples, shrine prostitution) (NRSV),
(b) feminine call boys (catamites) (NKJV),
(c) feminised eunuchs (Philo, Josephus).
The condemnation against μαλακος is available today for married homosexuals, intersex and transsexuals. These people must live celibate lives based on the Biblical perspective. The same condemnation applies to anyone who changes their sex assigned at birth , whether it be normal genitalia in transsexual cases or ambiguous genitalia in intersex cases. That is, the main idea condemned in μαλακος is the act of changing one's birth gender in any manner (whether by abusing it by sexual immorality or by changing its outward form to make it appear like the opposite sex). This means that homosexual sex is sin and that any one who undergoes sex reassignment surgery (whether the person is transgender or intersex) is condemned. The bodily gender even in its birth defect state is not to be corrected by doctors but to be corrected by the resurrection through Christ alone (Phil 3:20-21).
