This is steampunk, so assume a non-relativistic, non-quantum world (but more on that shortly).
I want a material that insulates against acceleration but not gravity.
This is the material one would use to line the walls of a cannon-launched spacecraft.
Let's assume that the insulation is not perfect. It reduces the acceleration felt by occupants, and a thicker layer provides better insulation. After all, I don't need complete inability to feel acceleration, it just has to be feasible to reduce accelerations of 1000g or more to something a human can survive. I expect the not-100% protection won't matter much to the physics, just mentioning it for completeness.
I haven't determined what happens if you don't insulate all sides of a capsule, or what happens if you bore a hole in the insulation.
Note in what sense I mean "insulates against acceleration". It doesn't mean "objects inside the container cannot be accelerated". It means "objects inside the container are accelerated along with it without feeling a force from the walls". That is, the insulation (if it were perfect) causes the interior to be an inertial reference frame regardless of its motion.
Because it insulates against acceleration, it also insulates against free-fall. If you were in orbit in such a spacecraft, you could walk on the floor; that is, the direction of the Earth would feel like down. But your weight pressing on the floor must not affect the trajectory of the spacecraft; how? I want to replicate how gravity worked in From the Earth to the Moon. The crew felt gravity except at the point where the gravity of the Earth and Moon cancelled.
As that points out, occupants are not insulated against the gravity of bodies outside. I assume that the outside world is also not insulated against the gravity of objects inside.
This material doesn't make accelerating the whole spacecraft any easier. As the previous paragraph notes, the craft as a whole affects and is affected by gravity in the same way a craft of the same mass without the insulation would be. Also, the inertial mass of objects placed inside the container can still be detected from the outside.
Clarification: The material does not just damp large accelerations. You can move inside normally. That is, a force exerted by one object inside on another object inside has the same effect it normally would. Only forces exerted on the outside of the container cause the specified effects inside.
The material is passive; it does not require a power source.
What are the unintended consequences of this?
I don't want this material to permit perpetual motion. It should be valuable, but not THAT valuable. A material that insulates against gravity would allow a perpetual motion waterwheel. I've avoided that, but I expect there may be other weird ways to get there.
That is, forget about Einsteinian relativity. This does weird things relating to Galilean/Newtonian relativity.
To restate, since I don't know if I got through: I'm looking for an interpretation of this material based on a 19th century understanding of acceleration and gravity, not a modern one. This is a world where the ether exists - not that I know exactly what that means, given that 19th century concepts of it were inconsistent and unclear. Giving something a name doesn't explain it. So I don't know whether I'm hoping for an explanation tied into the properties of ether or one that doesn't depend on them. I could express my goal as "I want something that, in a 19th century physics context, is more unobtainium than handwavium. And then I want to know the logical consequences." I know that isn't very technical.