In Islam cousin marriage is quite popular and widely acceptable. Cousin marriages, especially among first cousins, are a potentially harmful practice because the children born out of such marriages suffer from many genetic disorders. A comprehensive article about this debilitating practice among Muslims can be read HERE.
In fact, Dr. Mahathir the former Prime Minister of Malaysia was so concerned about the first cousin marriages among the Muslims in Malaysia that he wrote a book, The Malay Dilemma. In this book Dr Mahathir postulated that one of the main reasons for the absolute backwardness of Malays is due to their practice of in breeding. He was a medical professional. He wrote that because of in breeding the Malays have a very limited genetic pool.
Predictably, after the first publication of The Malay Dilemma, the Malaysian Government banned it, and Dr Mahathir was expelled from the Malaysia’s most dominant Muslim party UMNO (United Malays National Organisation). Malaysian Law stipulates that all Malays are, by definition, Muslims. A few years later, Dr Mahathir was again admitted into UMNO, and he finally became the UMNO president, but his book The Malay Dilemma remained proscribed. Only after Dr Mahathir became the Prime Minister of Malaysia, the ban on this controversial book was lifted, and republished in 1981.
Like it or not, Incest in Islam is alive and kicking well as can be illustrated from several verses of the Qur'an. The various interpretations, often contradictory, just prove that these words could not be from Allah. Allah cannot be so dim-witted not to know what is best for His Ummah. All knowing, almighty Allah cannot be so careless that He would leave His words in such a manner that what one group of Muslims means to be halal may be death to another group of Muslims. The topic of incest in Islam is such a dangerous game. It also possible that the inherent backward of the Muslim in general might be rooted in their limited genetic pool because of incestuous marriage practiced in many Islamic nation.