Nuts have little effect on the sound, so really only the hardness is relevant for them.
For a saddle, you have to look into a material's acoustic properties. You have to try to figure out what sort of impedance (the resistance to certain frequencies) and its pass-through (the frequencies that get transmitted to the bridge and then to the top) it has. And a few other things...
Look at
the chart here for some acoustic properties of common materials. The first figure, the longtitudinal velocity is basically the speed of sound in that material (in air it's about 331-350m/sec. So aluminum is much faster - at 6,700 m/sec). If you look at the woods (and
here too), you'll see wood is in the 4,000-5,000 m/sec range. Longtitudinal waves are simple compression waves.
The other thing to consider is the elasticity of the material (
Young's Modulus). The material has to bounce back quickly after compressing, or else it can't transmit the next wave in time. Low elasticity means higher impedance. Rubber is slow, aluminum is fast. But brass is faster - which is in part why it's a good acoustic material. Wood is fairly slow. That means it has more inertia (low elasticity means higher inertia: the material is reluctant to change its state).
Shear waves are transverse waves, moving perpendicular to the longtitudinal waves (they look like the sine wave created in the instrument's string). These are slower, so they don't arrive at the same time as the longtitudinal waves (there are shear waves in solids, but not gases or liquids, by the way). So these create overtones and harmonics, as well as giving some duration to the tones. These waves bounce back (and depend on the elasticity to do so).
And finally there's density. A dense material generally transfers the waves better, faster and with more fidelity than a less dense material. Denser materials can transmit a wider range of frequencies, especially those in the treble range.
Got that?
Soapstone doesn't have the elasticity, but it does have a fair density compared to other stones. However, it also has a high heat absorption capacity with a low dispersal of that heat, which makes me wonder if acoustic energy will be wasted by conversion into mechanical energy. In fact,
some builders use soapstone because it absorbs sound, rather than reflects it.
So I'd say: try it. If you're looking to make a shrill or bright uke more mellow, it should work. In fact it might make an interesting material for a banjo uke bridge. But because it is soft, it may wear the string slots faster than other materials. I don't think it's the best material, but it's decorative and might be able to modify a sound quite nicely.