I don’t see how anything non-Newtonian would be better against sudden sounds. In fact it would be worse, as they’d get more solid and thereby transmit MORE of the noise you’re trying to block out. Or maybe they only get more rigid but their sound transmission properties don’t change at all. Either way, sounds somewhat pointless.
The only way I can think that something like this would work would be to have a molded vacuum chamber as an ear plug, with a specifically engineered sound transmission bridge inside. With too much energy trying to go through, it would break. But I doubt it would be quick enough to be effective, and they’d also be one time use, and extremely fragile.
It’s a bit oversimplified, actually. Sound bounces off of discontinuities in the medium, which is why foam works. You just have to control scattering somehow.
The big problem with using oobleck or whatever is it responds to shear, and shear can’t travel through air. You could use it for earthquake protection, though, or if you could channel compressive waves from the air into shear form using a fancy bridge like in OP.
There are lots of strange options besides newtonian fluids. Would be interesting to see how dilatant, peusdoplastic, thixotropic etc react to sounds. Perhaps there is a way to make a material that allows quiet sounds to pass through and blocks all the loud ones. My guess is that dilatant liquids should be a good candidate.
A quick search tells me this have to do with shear forces. Sound would be entirely compressive, so those material properties would have no effect, or at least not change due to sound levels.
That’s unfortunate. Just like OP, I would have really liked the idea of using a non-newtonian fluid to filter out certain types of sounds without using electricity. Well, I guess, we’re back to active noise canceling then.