Can dress be so important that its violations may put a man or a woman into hellfire? Let us read.

Allah T'ala says in the Holy Quran:

يَا بَنِي آدَمَ قَدْ أَنزَلْنَا عَلَيْكُمْ لِبَاسًا يُوَارِي سَوْءَاتِكُمْ وَرِيشًا وَلِبَاسُ التَّقْوَىَ ذَلِكَ خَيْرٌ ذَلِكَ مِنْ آيَاتِ اللّهِ لَعَلَّهُمْ يَذَّكَّرُونَ

(7:26) 0 Children of Adam!  Indeed We have sent down to you a garment which covers your shame and provides protection and adornment. But the finest of all is the garment of piety. That is one of the signs of Allah so that they may take heed.
By referring to an important aspect of Adam and Eve's story, the attention of the people of Arabia of those days was drawn to the evil influence of Satan upon their lives. Under Satan's influence they had begun to see dress merely as a shield of protection against the inclemencies of the weather and as a means of adornment. The basic purpose of dress to cover the private parts of the body - had receded into the background. People had no inhibition about the immodest exposure of the private parts of their body in public. To publicly take a bath absolutely naked, to attend to the call of nature on thoroughfares, were the order of the day. To crown it all, in the course of Pilgrimage they used to circumambulate around the Ka'bah in stark nakedness. Women even surpassed men in immodesty. In their view, the performance of religious rites in complete nudity was an act of religious merit.
Immodesty, however, was not an exclusive characteristic of the people of Arabia. Many nations indulged in it in the past, and many nations continue to indulge in it even now. Hence the message embodied in these verses is not directed just to the people of Arabia. It is rather directed to all men. Mankind, which is the progeny of Adam, is warned against this particular aspect of Satanic influence on their lives. When men show indifference to God's Guidance and turn away from the Message of the Prophets, they virtually place themselves at the mercy of Satan. For it is Satan who makes them abandon way's that are consistent with true human nature and who leads them to immodesty in the same way he did with Adam and Eve. Were man to reflect on this, it would become quite evident that when he is deprived of the guidance of the Prophets, he cannot even appreciate, let alone fulfil, the primary requirements of his true nature.
يَا بَنِي آدَمَ لاَ يَفْتِنَنَّكُمُ الشَّيْطَانُ كَمَا أَخْرَجَ أَبَوَيْكُم مِّنَ الْجَنَّةِ يَنزِعُ عَنْهُمَا لِبَاسَهُمَا لِيُرِيَهُمَا سَوْءَاتِهِمَا

إِنَّهُ يَرَاكُمْ هُوَ وَقَبِيلُهُ مِنْ حَيْثُ لاَ تَرَوْنَهُمْ إِنَّا جَعَلْنَا الشَّيَاطِينَ أَوْلِيَاء لِلَّذِينَ لاَ يُؤْمِنُونَ
(7:27) Children of Adam! Let not Satan deceive you in the manner he deceived your parents out of Paradise, pulling off from them their clothing to reveal to them their shame. He and his host surely see you from whence you do not see them. We have made satans the guardians of those who do not believe.
These verses bring into focus several important points.
First, that the need to cover oneself is not an artificial urge in man; rather it is an important dictate of human nature. Unlike animals, God did not provide man with the protective covering that He provided to animals. God rather endowed man with the natural instincts of modesty and bashfulness. Moreover, the private parts of the body are not only, related to sex, but also constitute 'sawat' that is, something the exposure of which is felt to be shameful. Also, God did not provide man with a natural covering in response to man's modesty and bashfulness, but has inspired in him (see verse 26) the urge to cover himself. This is in order that man might use his reason to understand the requirements of his nature, use the resources made available by God, and provide himself a dress.

Second, man instinctively knows that the moral purpose behind the use of dress takes precedence over the physical purpose. Hence the idea that man should resort to dress in order to cover his private parts precedes the mention of dress as a means of providing protection and adornment to the human body. In this connection man is altogether different from animals, With regard to the latter, the natural covering that has been granted serves to protect them from the inclemencies of weather and also to beautify their bodies. However, that natural covering is altogether unrelated to the purpose of concealing their sexual organs. The exposure of those organs is not a matter of shame for them and hence their nature is altogether devoid of the urge to cover them. However, as men fell prey to Satanic influences, they developed a false and unhealthy notion about the function of dress. They were led to believe that the function of dress for human beings is no different from that for animals, viz., to protect them from the inclemencies of weather and to make them look attractive. As for concealing the private parts of the body, the importance of that function has been belittled. For men have been misled into believing that their private parts are, in fact, like other organs of their body. As in the case of animals, there is little need for human beings to conceal their sex organs.

Third, the Qur'an emphasizes that it is not enough for the dress to cover the private parts and to provide protection and adornment to the human body. Man's dress ought to be the dress of piety. This means that a man's dress ought to conceal his private parts. It should also render a man reasonably presentable - the dress being neither too shabby and cheap nor overly expensive and extravagant relative to his financial standing. Nor should dress smack of pride or hauteur, or reflect that pathological mental state in which men prefer characteristically feminine dresses and vice versa: or that the people belonging to one nation mimic people of other nations so as to resemble them, thereby becoming a living emblem of collective humiliation and abasement. The Qur'anic ideal can only be achieved by those who truly believe in the Prophets and sincerely try to follow God's Guidance. For as soon as man decides to reject God's Guidance, Satan assumes his patronage and by one means or another manages to lead him into error after error.

Fourth, the question of dress constitutes one of the numerous signs of God which is visible virtually throughout the world. When the facts mentioned above are carefully considered it will be quite clear as to why dress is an important sign of God. (Tafheemul Quran)