Yes, it's true that the Bible is more anti-gay that the Quran, since the Bible commands believers to kill homosexuals while the Quran does not. And yet a majority of U.S. Christians believe homosexuality is morally acceptable, and very few believe that homosexuals should be punished with death. The same cannot be said about modern Muslims.
So if the Bible is more anti-gay than the Quran, why are Muslims more anti-gay than Christians? The answer to that question is simple. His name is Muhammad (PB&J be upon him).
Muslims believe that Muhammad was the perfect and final messenger of God and that his words, thoughts, and actions (as recorded in the sunnah) should be obeyed, followed, and imitated by everyone. Although there is some disagreement among Muslims about which stories (hadith) about Muhammad are authentic, all describe a Muhammad who was vehemently and violently anti-gay.
Here are some examples from the hadith.
The Prophet (peace be upon him) said: If you find anyone doing as Lot's people did, kill the one who does it, and the one to whom it is done. - Abu Dawud 38:4447And then there's this from Islam Question and Answer:
If a man who is not married is seized committing sodomy, he will be stoned to death. - Abu Dawud 38:4448
The Apostle of Allah (peace be upon him) cursed the man who dressed like a woman and the woman who dressed like a man. - Abu Dawud 32:4087
The Sahaabah were unanimously agreed on the execution of homosexuals, but they differed as to how they were to be executed. Some of them were of the view that they should be burned with fire, which was the view of ‘Ali (may Allaah be pleased with him) and also of Abu Bakr (may Allaah be pleased with him), as we shall see below. And some of them thought that they should be thrown down from a high place then have stones thrown at them. This was the view of Ibn ‘Abbaas (may Allaah be pleased with him).You just can't get more ant-gay that that!
And yet there is hope for reform in Islam. Christians and Jews learned long ago to ignore the cruel command in Leviticus 20:13. Muslims could do the same with similar statements in the hadith. But until the vast majority of Muslims do that, Islam will be more anti-gay than Christianity.