One-way magnetic shielding? Is there such a thing as a material that allows magnetic/electric fields to pass one way but not the other?
An analogous example would be a one-way mirror where light can pass through it one way but not the other.
 A: In 2018, a team of researchers did in fact design a material that acts as a "magnetic diode", that is, one that allows the flow of a magnetic field in one direction, but not the opposite direction.
The paper is called
Circumventing Magnetostatic Reciprocity: A Diode for Magnetic Fields
by J. Prat-Camps, P. Maurer, G. Kirchmair, and O. Romero-Isart.  The article is in Physical Review Letters. Since not everyone has access to PRL$^1$, this is basic summary:
When current flows through a coil, a magnetic field is induced in the coil. A magnetic field can also be induced in another nearby magnetic coil of wire due to the first. Due to the laws of electromagnetism, this induction of magnetic field is symmetric. This means that the magnetic field will move from one coil to the second, and from the second back to the first.
The researchers wondered if there was a way they could break this reciprocity, such that the magnetic field could be induced one way only, and they found that this can be the case if both coils are placed in between the walls of a hollow rotating, conducting cylinder.
During a demonstration, researchers showed that when the cylinder rotates at a constant angular velocity, a magnetic field from one coil can induce a magnetic field in another coil of certain material, but not from the second coil back to the first$^2$.

As for electric fields, another team of researchers also in 2018, designed a two-dimensional, nanostructured material that behaves like a diode, that conducts and blocks electrical current using magnetism (i.e., not through the interface between two semiconductors as per standard diodes).
From that link:
"The diode is comprised of a two-dimensional, nanostructured material created by depositing a magnetic alloy, or permalloy, on the honeycomb structured template of a silicon surface. The material behaves like a diode without any application of an external magnetic field — magnetic charges in the material itself create the diode effect. What’s interesting about the material is that it dissipates significantly less power during conduction compared to an ordinary semiconducting diode."
"“In a surprise, we have found the diode-type rectification in nanostructured 2D honeycomb lattice, made of ultrasmall permalloy (Ni0.81Fe0.19) magnet,” the researchers write. “Electronic measurements on newly fabricated permalloy honeycomb lattice of ultra-small connecting elements (≈12 nm) have revealed unidirectional electrical properties without the application of magnetic field and with the output power of the order of ≈30 nW. In fact, magnetic field application changes the asymmetric behavior into a symmetric phenomenon. In zero field, electrical differential conductivity increases by more than two orders of magnitude for a modest unidirectional current application of ≈10 μA, compared to the negligible value near zero bias. Electronic measurement for the oppositely directed current yields a very small or negligible differential conductivity,” they say in one of the papers."
$^1$ Thanks to @StephenG for pointing out that there is a copy of the PRL paper on arxiv.org.
$^2$This seems to indicate that one of the most profound and deeply established ideas in electromagnetism, i.e., that mutual inductances are symmetric, is sometimes broken. However, this is not the case, and I would advise that one has a read of the paper to get an understanding of all of the physics at play in this situation.
A: Note that a "one way mirror" is actually two way. It is a partially reflective, partially transmissive mirror that works the same either direction.
It is placed between two rooms, one bright, the other dark. Observers on both sides see a combination of reflection from their own room and and transmitted light from the other room.
In the bright room, there is very little transmitted light and a lot of reflected light. That is, the bright room observer sees his reflection.
In the dark room, there is a lot of transmitted light and very little reflected light. The observer sees the transmitted light from the bright room.
