When can taste be used to help identify rocks?
You are correct about halite and sylvite. I might add that carnallite also has an extremely bitter taste. These three minerals are chlorides and dissolve very easily, so that may be a part of the issue here.
Differentiating mudstone (clay) from siltstone is actually not about taste, but rather about texture. Note that this can be misleading. If you have a rock with 70% clays and 30% sand (or silt), you are going to feel the silt, giving it a higher proportion in your estimate, unless you have enough experience to consider this bias.

I would also like to note the dangers in tasting rocks. Although not common, some minerals are radioactive. Also some minerals contain lead, mercury and other hazardous elements. Some minerals may also be contaminated by anthropogenic pollution. So be careful with tasting rocks.