“This sin, the impact of which makes one’s skin crawl, which words cannot describe, is evidence of perverted instincts, total collapse of shame and honor, and extreme filthiness of character and soul… The heavens, the Earth, and the mountains tremble from the impact of this sin. The angels shudder as they anticipate the punishment of Allah to descend upon the people who commit this indescribable sin.”  Dr. Abdul Aziz Al-Fawzan, The Evil Sin of Homosexuality

Islam doesn’t merely disapprove homosexuality, it terms it as a vile and evil sin that is considered worse than fornication and adultery and is punishable by stoning to death.

The homosexual person goes against the natural fitrah (disposition) which Allah has created for mankind and Allah has warned against falling into such evil sins. The homosexuality causes various diseases that no one can deny. It causes families to break up and may lead a person to leave his work and family because he is occupied with such perversions. A person is left with no shame and honor.  Allah has forbidden it and any sane, reasonable and modest person would not question on the prohibition of this immorality. As a Muslim, we must believe that whatever Allah has forbidden is indeed harmful to mankind and vice-versa.
Ibn al-Qayyim said: 
Both of them – fornication and homosexuality – involve immorality that goes against the wisdom of Allaah’s creation and commandment. For homosexuality involves innumerable evil and harms, and the one to whom it is done would be better off being killed than having this done to him, because after that he will become so evil and so corrupt that there can be no hope of his being reformed, and all good is lost for him, and he will no longer feel any shame before Allaah or before His creation. The semen of the one who did that to him will act as a poison on his body and soul. The scholars differed as to whether the one to whom it is done will ever enter Paradise. There are two opinions which I heard Shaykh al-Islam (may Allaah have mercy on him) narrate.” 
(Al-Jawaab al-Kaafi, p. 115). 

Quranic evidence:

"...For ye practice your lusts on men in preference to women: ye are indeed a people transgressing beyond bounds.... And we rained down on them a shower (of brimstone)" –Quran (7:80-84)

From this verse, we can conclude that the man who prefers a man over women are indeed transgressors and liable to punishment and their punishment is death by stoning as what happened to the people of Lot. It is an interpretation of the majority of Muslim scholars that the “raining of stones” means the destruction of such people by stoning. (Inexplicably, the story is also repeated in three other suras: 15:74, 27:58 and 29:40).

"Will ye commit abomination such as no creature ever did before you?"  Quran (7:18)

This verse clearly establishes that homosexuality as a different form and much worse than the adultery and fornication. According to Arabic grammar, it is called as worst sin whereas other forms of Zina are considered as great sins. From here we can conclude that it is indeed a great evil.

Other Quranic evidence:

“Verily, you practice your lusts on men instead of women. Nay, but you are a people transgressing beyond bounds (by committing great sins)’” (al-A’raaf 7:80-81)
“Verily, We sent against them a violent storm of stones (which destroyed them all), except the family of Loot (Lot), them We saved in the last hour of the night” (al-Qamar 54:34)

“And (remember) Loot (Lot), when he said to his people: ‘you commit Al‑Faahishah (sodomy the worst sin) which none has preceded you in (committing) it in the ‘Aalameen (mankind and jinn)’” (al-‘Ankaboot 29:28)
Allah mentions in glorious Quran that none of the mankind or Jinn’s had committed such worst sins before the people of Lut (AS) and this was the reason for their destruction. It is a clear warning of Allah aza-wa-jal to mankind to stay away from it.
 “And (remember) Loot (Lot), We gave him Hukm (right judgment of the affairs and Prophethood) and (religious) knowledge, and We saved him from the town (folk) who practiced Al‑Khabaa’ith (evil, wicked and filthy deeds). Verily, they were a people given to evil and were Faasiqoon (rebellious, disobedient to Allaah)” (al-Anbiya’ 21:74)
 The deed of homosexuality is termed as a vile, evil and filthy deed by Allah aza-wa-jal. This is the immorality which has no place in Islamic society.
Evidence from Hadith and Sira:

It was narrated that Jaabir (may Allaah be pleased with him): “The Prophet (peace and blessings of Allaah be upon him) said: ‘There is nothing I fear for my ummah more than the deed of the people of Loot.’” (Narrated by al-Tirmidhi, 1457; Ibn Maajah, 2563.)
It was narrated that Ibn ‘Abbaas said: “The Prophet (peace and blessings of Allaah be upon him) said: “… cursed is the one who has intercourse with an animal, cursed is the one who does the action of the people of Loot.” (Narrated by Ahmad, 1878.)

It was narrated that Ibn ‘Abbaas said: “The Prophet (peace and blessings of Allaah be upon him) said: ‘Whoever you find doing the deed of the people of Loot, kill the one who does it and the one to whom it is done.” (Narrated by al-Tirmidhi, 1456.)

In most of the Islamic countries where shariah law is strictly applied, homosexuals are beheaded, burned or killed by stoning or throwing from rooftops.
According to Serge Trifkovic:
Mohammed’s (saw) first successor Abu Bakr (RA) reportedly had a homosexual burned at the stake. The fourth caliph, Mohammed’s (saw) son-in-law Ali (RA), ordered a sodomite thrown from the minaret of a mosque. Others he ordered to be stoned. One of the earliest and most authoritative commentators on the Koran, Ibn ‘Abbas (died 687) blended both approaches into a two-step execution in which “the sodomite should be thrown from the highest building in the town and then stoned.

We as a Muslim should never support such LGBT or homosexual groups and should never think leniently about them. They don’t deserve sympathy and should be condemned. Neither should a Muslim engage in such evil practices unless he wishes to dwell in the pit of fire for the eternity.
And Allah knows best.