Any judge allowing the use of any law not found in U.S. or applicable state statute has declared himself/herself as being guilty of malfeasance. Period. 14th Amendment: “no state shall ... deny to any person within its jurisdiction the equal protection of the laws”. No wiggle room. No possibility of misunderstanding.
Really, only statues, not the Constitution of the United States or the relevant state constitution, not treaties the U.S. had entered into? (Okay I know, you really meant to include that: I'm just yanking your proverbial chain.)
I agree, but with third exceptions. First, the biggest, judges should apply Common Law, when statutes are ambiguous or in areas where only case-law applies. The Founders assumed English Common Law as the basis for many notions found in the Constitution. Abandoning Common Law in favor of the whims of majorities in legislatures has actually been a detriment to American liberty. In fact, when no U.S. precedents are available, considering precedents from other Common Law countries (the U.K; Canada, excluding Quebec on civil cases; Australia; or New Zealand) is entirely appropriate.
Second, if a state has statutory provisions for parties to a dispute to select a binding arbiter whose decisions can be enforced by the courts, provided the decisions do not violate Constitutional or statutory protections, the courts in such circumstances may need to consider the basis for the binding arbiter's decision, even if that basis is Latin or Orthodox canon law, rabbinical law, some African tribe's law, or yes, even Sharia law.
Third, in the case of disputes naturally involving either canon law or its equivalent (property and personnel disputes within religious institutions, for instance) or foreign law (disputes involving foreign corporations in which actions both inside and outside the U.S. matter to the dispute, for instance) it is appropriate for courts to consider the other legal system.
But in all cases, the courts jolly well ought not violate or abrogate the Constitutional, statutory or Common Law rights of parties to a dispute simply because some other system of law is relevant to the dispute. (I would note that some courts lately, the Indiana Supreme Court being an egregious example, don't seem to need any help from consideration of foreign law to abrogate simultaneously or Constitutional and Common Law rights.)