The AP has an interesting story on the subject (though I don’t know anything about Islamic law on this score, and thus can’t vouch for its accuracy). For instance,
Traditional, closed adoption violates Islamic jurisprudence, which stresses the importance of lineage. Instead, Islam has a guardianship system called kafalah that resembles foster care, yet has no exact counterpart in Western law.
The differences have left young Muslims with little chance of finding a permanent Muslim home in America….
As Muslim communities become more established in the United States, pressure is building for a re-examination of Islamic law on adoption.
Refugee children from Afghanistan, Iraq and elsewhere are being resettled here. Muslim couples who can’t conceive want to adopt, but don’t want to violate their faith’s teachings. State child welfare agencies that permanently remove Muslim children from troubled homes usually can’t find Muslim families to adopt them because of the restrictions in Islamic law….
When an orphan reaches puberty, the Islamic prohibition against mixing of the sexes applies inside the home of his or her guardians. Muslim men cannot be alone with women they could potentially marry, and women must cover their hair around these men. Islamic law sets out detailed rules about who believers can and cannot marry, and an orphan taken in from another family would not automatically be considered “unmarriageable” to his siblings or guardians.
For these reasons and others, Muslim countries only rarely allow international adoption….
Note that, at least based on the story, the question is not one of whether American law should in some measure adapt to accommodate Muslim practices. (For more on this religious exemption issue, which arises in other contexts, see here.) Rather, it’s whether Muslim cultural practices and religious interpretations ought to be altered or adapted to make adoption, and in particular adoption in Western societies, easier. Thanks to Fred Ray for the pointer.