Critics cite narrations prescribing death for homosexual acts to call Islamic law cruel. The most graphic of these reports is graded weak by hadith scholars, the classical penalty required a standard of proof that made it almost impossible to apply, and Islam draws a clear line between an act it prohibits and a person, whom it never licenses anyone to harm.
The most-quoted narration is weak
The narration most often thrown into these debates - "kill the one who does it and the one to whom it is done" (Sunan Abi Dawud 4462) - is classed as weak (da'if) by hadith critics, including Shaykh al-Albani. A weak report does not establish a ruling, so it is a poor foundation for the "Islam commands killing" charge. Muslims are not bound to defend a narration the scholars themselves questioned.
The act is prohibited - but the courtroom bar was near-impossible
Islam does regard the act of the people of Lot as a serious sin; that is not in dispute. But a sin being grave is not the same as a punishment being easy to impose. Classical jurists differed on the exact penalty, and those who held a severe one still required the same evidentiary standard as for adultery: four upright witnesses to the act itself, or a free, repeated confession the person could withdraw at any time. In practice this bar is almost never met. The law's aim was deterrence and the protection of public decency, not hunting individuals - which is why such cases are virtually unknown in Islamic legal history.
A private inclination is not a crime, and mercy is the rule
Islam does not police people's inner feelings, and it commands the covering of faults rather than exposure. The Prophet (PBUH) said:
Whoever conceals the faults of a Muslim, Allah will conceal his faults on the Day of Resurrection.
Sahih Muslim
The door of repentance is always open, and no ruling gives an individual, a mob, or a family any right to harm anyone. Every human being retains the dignity the Quran affirms for all:
And We have certainly honoured the children of Adam.
Quran 17:70
So the honest picture is not the cartoon of a faith eager to execute. Islam holds a moral position on a particular act - as many traditions historically did - while resting its harshest penalties on evidence so demanding they were effectively unenforceable, and while insisting on privacy, mercy, and the worth of the person.