Answer 1
No true Muslim calls Jews the descendents of apes and pigs. The Qur'an mentions three groups of Jews.
One group broke the rule of Sabath. (Saturday)
The second group didn't defy the command of Almighty God itself, but didn't warn group One to refrain from that bad activity.
The third group warned the first group to refrain from defying the Command.
First two groups pushed the third group to the other side of the wall. Almighty God turned the first two groups in the form of Apes and pigs. But these apes and pigs died within a few days of their punishment. So there are no descendents of those Jews who were turned into apes. No civilized person should call others the descendents of apes and pigs. All humans are the off-spring of Hazrat Adam (AS) and Hazrat Eve (AS).
Answer 2
Yes, some do.
The question is "Do Muslims say..." not "Do allMuslims say..." because there are certainly Muslims (persons who identify themselves as and are typically idenftified as Muslims) who do say that Jews are apes and swine and they claim that their view is Qur'anic. There have also been numerous Islamic leaders, Muslims with political and religious clout, who make this assertion. Some of these leaders include: PA Mufti Muhammad Hussein, Sheikh Muhammad Al-Tawil - a teacher in Al-Aqsa Mosque school, Saudi school textbooks, Mohammed Morsi, Hassan Nasrallah, Sheikh Eid Abdel Hamid Youssef - Egyptian lead sheikh in 2009, Al-Azhar Sheikh Muhammad Sayyid Tantawi, and Saudi sheikh Abd Al-Rahman Al-Sudayyis.
The leaders who make these assertions, base their views on interpretations of the Qur'anic verses Q: 2:63-65, 5:59-60, and 7:166, all of which refer to God turning the Jews who violated their commandments into apes and pigs. Unfortunately, many Muslims (especially more zealous Anti-Semities and Anti-Zionists among them) do not use the term "apes and pigs" to refer to this specific set of Jews, but use it to tar Jews in general.
It is worth noting that there are three interpretations of what happened to the Jews discussed in Q: 2:63-65 because the Qur'an itself does not provide an outcome. There is the view, as mentioned in Answer 1, which is the dominant view, holding that the Jews who were turned into animals died within three days without having any offspring. There is the view that the Jews who were turned into animals remained animals and reproduced as animals, contributing to the animal population, such as brought up by Al-Jahiz in "The Book of Animals" who notes that the reason why lizard hands may look like human hands is because lizards might be descended from the oath-breaking Jews. Finally, there is the view that the oath-breakers were changed back from being animals to being humans again and that the Jews of today are their descendants. This view is becoming increasingly popular as it provides a perfect corollary to Anti-Zionist sentiment in the Islamic World. (The argument works that the State of Israel is inherently immoral as a country since Jews are inherently immoral as a people.)
Other sheikhs have noticed the failure by Islamic Leaders to contextualize the Qur'anic verses and reprimand by holding to third approach.
Sheikh Qaradawi in Egypt has said: "I denounced some contemporary religious preachers, who curse the Jews and the Christians, saying: "Allah, annihilate the Jews and the Christians." Where did this come from? There are Jews and Christians in our Muslim countries. There are Copts in Egypt, and Christians in Syria. So how can you curse them? Not only that, but they curse: "Allah, turn their children in orphans," "Allah, destroy their homes." Who sanctioned such prayers?...I denounced some people who said that the Jews are the offspring of apes and pigs. That's not true. When God transformed some people into apes and pigs, they did not have any offspring, as is written in the Al-Muslim compilation."
Tawfik Hamid has also noted this issue, making it his "letter C" on his "ABCs Test of Radical Islam" - "Calling Jews Apes and Pigs".
As to the position raised in Answer 1 that "true Muslims believe x", that is a "No True Scotsman fallacy". Typically, a Muslim is any person who says شهادتين (Shahadatayn) - the two testimonies (that there is only one God and that Mohammed is His Messenger) - with conviction. All of the people cited above do exactly that. Additionally, there is a scholarly position which holds what they believe. Admittedly, it is a controversial doctrine, but it is not as if those Muslims who say that Jews are the descendants of apes and pigs do not have ground to stand on; they do.
Below in the Related Links are several instances of Islamic leaders calling the Jews "descendants of apes and pigs".
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It comes from Q: 2:63-65, 5:59-60, and 7:166, all of which refer to God turning the Jews who violated their commandments into apes and pigs. Unfortunately, many Muslims (especially more zealous Anti-Semities and Anti-Zionists among them) do not use the term "apes and pigs" to refer to this specific set of Jews, but use it to tar Jews in general.