Believe it or not there are gay Muslim groups who do cite Quranic verses and Hadiths which show tolerance for gay people. I generally find them as unpersuasive as the gay Christians and gay Catholics who make similar arguments regarding the Church, but they sincerely believe it.
It’s also worth noting that because for the longest time people in the Muslim world didn’t think of gays as an entirely separate category and the idea of gay identity was alien to them(which was largely true in the West up until the late 19th Century) many had vastly different attitudes towards behavior that most of us in the West would consider “gay” and well up until the 1960s or 70s most of the Middle East, particularly Lebanon and Morocco was for practical purposes less homophobic than the West.
That’s not to say that being openly gay was a good idea or tolerated, but there was such a strong society wide denial of their existence that gay bars could operate much more openly than they could in the US without being afraid of police raids and so long as one was discrete you could bang boys not the side and no one would care(granted being a bottom was considered vastly, vastly worse than being a top which still persists to this day).
In fact, it was very common for many diplomatic personnel from the West to be gay because they could feel safer and not have to worry about hiding the way they had to in the US, Canada, or UK.
As my mother, an American woman said, “Being openly gay in the 60s and 70s was much safer in the West than Iran, but being a closeted gay was vastly better in Iran during the same period.”
Sadly, this has dramatically changed since the 70s for the worse in most of the Middle East.
That said, even today you’ll still see such attitudes persisting. Yes, “gays” are banned from the Turkish army but only if you’re a bottom and while few will admit it I wouldn’t be surprised if more members of the Basij in Iran have engaged in ass play than gay men in the US(many of whom in my experience are scared to death of anal sex).
None of what I’ve said is meant as an endorsement of such attitudes obviously or a suggestion that being gay in the West isn’t clear, at this moment, better in the US than most of the Middle East, but it’s vastly more complex than many think and has more to do with history and culture than theology.