Why do chillies appear milder when combined with pineapple or yogurt?

If you clean your hands and cutting board with lemon juice (acid) after cutting up chillies that will dissolve the heat chemicals (capsicum) (base), but if you wash with soap and water (base) it will feel even hotter. Lemon juice is one of the recommended washes for pepper spray, which has the same capsicum as chilies. So, eating lemon or other acid with the chilies might neutralize some of their heat as well.

It seems the capsicum is a base, so soap which is basic just leaves it untouched, and an acid neutralizes it. Milk is slightly acidic, so it may neutralize the capisicum in this way as well. Likely it also engages the molecules in some other way to keep them from sticking to the skin. I have heard the same as Micki about milk. Rinsing your hands in milk will get the hot stuff off better than soap and water.

As far as the website and milk producer claims go about the casein being lipophilic, that doesn't really explain it. Soap is lipophilic too, which doesn't work. If this were true, egg or meat or beans would work too. Maybe they do?? Don't know, but don't think so.

Pineapple and Pappaya both have proteolytic (breaks down proteins) enzymes that I have heard work to get the capsicum off your hands when cutting or eating hot peppers, but I couldn't find any evidence of that. Just guessing that the enzymes loosen the bond of the capisicum to skin linings in the mouth and gut. That would help explain your observations, though.

Food technology papers would have a more specific answer.

The California Milk Processors Board, the "Got Milk?" people, claims there's scientific evidence that casein, the principal protein in milk, removes from the mouth the hot chemical in chiles, thus providing immediate relief.

...though they don't say why.

And, I could find nothing about a relaiionship with pineapple, though some claimed that eating chocolate could provide some relief

Chillies contain a substance called "capsaicins". They are the reason behind chillies distinctive hot taste. They work by stimulating those areas of the tongue that are sensitive to heat and pain. I am not sure about yogurt or pineapple, but I suspect that they contain substances that nullify capsaicins.

The brain is only allots itself only a certain quantity of capacity for sensing from the tongue. So if there are more than one possible taste, each has to be diminished enough to allow some of the other to appear. That's our "sorting mechanism". The brain is not a passive receptor of data. It takes the mass, sorts it, and fits it all into a sensible pattern. It needs to be economical about doing this, respecting the vastness of the data and avoiding overload or imbalance.

Ohh Who lives in a pineapple under the sea "Spongebob squarepants" Absorbant and yellow and porous is he "Spongebob Squarepants" If nautical nonsense be something you like "Spongebob Squarepants" Then flop on the deck and plop like a fish "Spongebob Squarepants"