Cool, that is good Islam teaches its adherents to be kind to most animals. Although the Bible tells us that we are God's stewards and that God cares for the sparrows, Islam is more explicit in teaching its followers to not harm animals. I commend that.
I still think, however, that halal and kosher forms of slaughter are not the least painful ways to kill animals that we eat. I think they are more humane than most methods used by other slaughterhouses, however, there are also non-Muslims who kill animals just as if not more humanely.
Does Islam's required kindness to animals extend to salamanders?
There are 5 animals we are permitted to kill on sight.Crows, Kites, Mice, Scorpions and Rabid Dogs (this is from Ahadith, none are mentioned in the Qur'an) but even when killing these it is to be done swiftly and with as little pain as possible. Hunting is forbidden in Islam except for food. So even with the "permitted" animals we are not to go out deliberately looking for them
Side Bar: The particular hadith was narrated/witnessed by 7 different people 6 of them specify RABID dogs. One of them left out the word rabid. That is the witness most hate sites quote without ever mentioning the other 6 witnesses.
There are ahadith that some people think command us to kill Salamanders
Salamander is mentioned in 4 ahadith compiled by Sahih Bukhari
1) Narrated 'Aisha the wife of the Prophet: Allah's Apostle called the salamander a bad animal, but I did not hear him ordering it to be killed." (Book #29, Hadith #57)
(2) Narrated Aisha: The Prophet called the salamander, a mischief-doer. I have not heard him ordering that it should be killed. Sad bin Waqqas claims that the Prophet ordered that it should be killed. (Book #54, Hadith #525)
(3) Narrated Um Sharik: That the Prophet ordered her to kill salamanders. (Book #54, Hadith #526)
(4) Narrated Um Sharik: Allah's Apostle ordered that the salamander should be killed and said, "It (i.e. the salamander) blew (the fire) on Abraham." (Book #55, Hadith #579)
From these Ahadith there does not seem to be a general permission or command to kill salamanders. but for some reason he told Sad bin Waqqas and um Sharik to do so.
But we do not know the conditions or reasons he told them to. Anyhow there is no command for all people to go around killing salamanders
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Even then we should do so swiftly and with minimal pain.