Do dishes used for preparing food need to be washed with soap

What type of stone, lava, marble, granite? Bleach makes for a nice general purpose disinfectant, as it degrades on its own over time. Let the thing soak in bleach (1 part bleach 9 part water) for a few days then boil again, and you should be good to go; once you find a pestle that fits.

Before we proceed, we should note that not all dirty dishes are created equal. There are a few "groups" with different chemical and physical properties.

• Sugar
  Probably the easiest of all as it will happily dissolve in water. A bit quicker in warm or hot water than in cold water (iced tea, anyone?), but not adverse to being washed off. We can probably ignore it for our further discussion.
• Starch, uncooked
  Pure starch will easily dissolve in cold water, but tends to form lumps in hot water as anyone trying to thicken a soup or sauce can attest. This means all starchy dishes, from your bread bowl to the spoon in your bag of flour needs to be rinsed cold (first) or you will end up with a glue-like substance clinging to your dishes, your rag, your brush, whatever. You need to create a suspension, that is tiny particles floating in your water instead of a sticky goo.
• Proteins, unheated
  Unheated, that means uncoagulated proteins, like the yolks in your breakfast egg or that cup with fat-free milk, even the cutting board of your meat are comparatively easy to dissolve in cool-to-lukewarm water - everything below their specific temperature at which they denaturize. This does not mean that they are clean after that because there are:
• Fats
  This is the one group that really, really needs some solvent, aka dishwashing liquid for simple chemical reasons: Fats are hydrophobic, they do not mix with water. Your soap binds with the fat molecules forming larger molecules, that are then soluble in water. Hotter water speeds up this process, similar to sugar dissolving faster in hot water. Plus food fats that are solid at room temperature turn liquid when warmed which helps the soap to "get" the fat molecules. No need to boil your hands, though.

Now unless you serve a very restricted breakfast, your dishes will likely contain something of each group above, so you need an adjusted approach:

Those dishes that have starchy and protein-rich components may benefit from a cool rinse first. Then your dishes can go in the sink with quite warm water - hotter speeds up the "loosening" of fats and other crusts, but you need not "boil" your hands, gloved or not.

Yet we still have to consider our nasty hitchhikers:

• Bacteria and their ilk
  Let's get one misconception out of the way first: Washing dishes, whether by hand or in a dishwasher, does not remove all bacteria. You can scrub and sanitize to your heart's content, your kitchen will never be truly sterile. And it doesn't have to. The human body deals well with some "intruders" on average, they can even be beneficial.
  What we want to do is to reduce the total amount of bacteria present and, if possible, eliminate those that are highly pathogenic. (Don't lick that raw chicken...!) Unfortunately, the suggestion of washing your dishes with really hot water to kill them is impractical at best - Salmonella dies at about 70C / 155 F¹, similar rules apply for Listeria.
  Bacteria doesn't come alone, it is on and in the food. So cleaning the dishes well and removing all residue will in fact rinse the bacteria right off and leave the very few that still might cling to a plate without food, causing many of them to die. Much more critical is the great bacterial breeding ground near your sink: Sponges and rags may contain far more pathogens than a random plate - your food is typically not contaminated to the hilt from the start. So make sure you rinse your dishes well after washing, consider air-drying or at least use a fresh towel.

¹ To be precise, it's a function over time and temperature, but that doesn't make much of a difference here.