No one can be legally bound by religious law because religious laws cannot be espoused by the government. If the parties agree to it, religious laws cannot conflict with criminal or civil laws under the First Amendment, it would be enforceable within the religious community. "(See Watson v. Jones, 80 U.S. 679 (1872) (“All who united themselves to such a body [the general church] do so with an implied consent to [its] government, and are bound to submit to it.”)."
Foreign or religious law can and should be used in certain situations. "For example, parties to a contract enjoy a great deal of leeway to establish binding agreements requiring contractual disputes to be submitted to arbitration. In their arbitration agreement, the disputing parties can bind themselves to use a particular arbitrator. Courts have held that arbitration agreements providing for what is commonly referred to as “biblically based mediation” (relying on specified principles of the Christian Bible) are enforceable."
There have been attempts to use sharia law where domestic relations are at issue. For example, "sharia in domestic courts is S.D. v. M.J.R., a New Jersey domestic violence case. In that dispute, a Muslim wife filed for a restraining order against her husband after several instances of physical abuse and non-consensual sexual intercourse. Though the trial court found that the defendant had engaged in sexual acts that were clearly against his wife’s wishes, it did not grant a final restraining order because the husband lacked the requisite criminal intent to commit sexual assault. This decision was based on the theory that the defendant acted based on his religious belief that a husband may demand to have intercourse with his wife whenever he desired. On appeal, the New Jersey Appellate Division overturned the trial court’s decision and remanded the case to the lower court for entry of a final restraining order. Noting that the case involved “a conflict between the criminal law and religious precepts,” the appellate court held that the defendant knowingly engaged in non-consensual sexual intercourse and thus could not be excused for his religious beliefs."
Also, the government is prohibited from interfering with religious activities.
"Proposals to ban sharia raise a serious dilemma for legal scholars and jurists because the composition of sharia remains debated among various Islamic sects and scholars. Without an authoritative body of law with specific parameters, courts may find themselves faced with a need to determine the precise principles of sharia and thus offer judgment on the content of a religious doctrine, which is generally impermissible under the First Amendment."
"In 1872, the Court recognized that matters of religious doctrine should be determined within the authority of the particular church and should be separate from any secular legal interpretation: The law knows no heresy, and is committed to the support of no dogma, the establishment of no sect. … "
All who united themselves to such a body [the general church] do so with an implied consent to [its] government, and are bound to submit to it. But it would be a vain consent and would lead to total subversion of such religious bodies, if any one aggrieved by one of their decisions could appeal to the secular courts and have them [sic] reversed. It is of the essence of these religious unions, and of their right to establish tribunals for the decision of questions arising among themselves, that those decisions should be binding in all cases of ecclesiastical cognizance, subject only to such appeals as the organism itself provides for*.
Thus, the Court established the principle that determinations of church doctrine and practice were to be free of government control well before it had even developed other aspects of its First Amendment jurisprudence. That general principle has since been cited by the Court in a number of First Amendment cases involving challenges of government interference in internal church matters."
http://www.fas.org/sgp/crs/misc/R41824.pdf
*(see Watson v. Jones, 80 U.S. 679 (1872), quoted in Presbyterian Church v. Hull Memorial Presbyterian Church, 393 U.S. 440, 446 (1969). See also Gonzalez v. Archbishop, 280 U.S. 1 (1929) (“In the absence of fraud, collusion, or arbitrariness, the decisions of the proper church tribunals on matters purely ecclesiastical, although affecting civil rights, are accepted in litigation before the secular courts as conclusive, because the parties in interest made them so by contract or otherwise.”).
