Sharia directs that women accused of adultery be stoned to death. This report does not explain why this woman was shot to death instead. In any case, putting adulterers (although usually only women are punished this way) to death is not “extremist”; it is Islamic law. The caliph Umar, one of Muhammad’s closest companions, even maintained that it was originally in the Qur’an:

‘Umar said, “I am afraid that after a long time has passed, people may say, “We do not find the Verses of the Rajam (stoning to death) in the Holy Book,” and consequently they may go astray by leaving an obligation that Allah has revealed. Lo! I confirm that the penalty of Rajam be inflicted on him who commits illegal sexual intercourse, if he is already married and the crime is proved by witnesses or pregnancy or confession.” Sufyan added, “I have memorized this narration in this way.” ‘Umar added, “Surely Allah’s Apostle carried out the penalty of Rajam, and so did we after him.” (Bukhari, vol. 8, bk. 82, no. 816)

“Allah’s Apostle” is, of course, Muhammad, who did indeed carry out stonings. Here is the hadith in which he challenges the rabbis about stoning, and in which there is amidst the barbarism and brutality a final act of love and compassion:

The Jews came to Allah’s Apostle and told him that a man and a woman from amongst them had committed illegal sexual intercourse. Allah’s Apostle said to them, “What do you find in the Torah (old Testament) about the legal punishment of Ar-Rajm (stoning)?” They replied, (But) we announce their crime and lash them.” Abdullah bin Salam said, “You are telling a lie; Torah contains the order of Rajm.” They brought and opened the Torah and one of them solaced his hand on the Verse of Rajm and read the verses preceding and following it. Abdullah bin Salam said to him, “Lift your hand.” When he lifted his hand, the Verse of Rajm was written there. They said, “Muhammad has told the truth; the Torah has the Verse of Rajm. The Prophet then gave the order that both of them should be stoned to death. (‘Abdullah bin ‘Umar said, “I saw the man leaning over the woman to shelter her from the stones.” (Bukhari, vol. 4, bk. 56, no. 829)

Even the monkeys practiced stoning, according to another hadith:

During the pre-lslamic period of ignorance I saw a she-monkey surrounded by a number of monkeys. They were all stoning it, because it had committed illegal sexual intercourse. I too, stoned it along with them. (Bukhari, vol. 5, bk. 58, no. 188)

Muhammad’s example is, of course, normative for Islamic behavior, since “truly in the messenger of Allah you have a good example for him who looks to Allah and the Last Day, and remembers Allah much” (Qur’an 33:21).

“Woman Shooting by Taliban Members in Baghlan,” BNA, March 18, 2020 (thanks to The Religion of Peace):