Which foods are certain to never cause food poisoning?

There is almost no food which is guaranteed to be safe. If it has nutritional value for a human, it has nutritional value for many microorganisms too, some of which are human pathogens.

So, out of the FATTOM rule, you can already throw out F: you cannot remove the food. A is also not a good candidate - no food is naturally acidic enough, and while there are foods preserved by acidity, an error in processing can lead to the food being dangerous. Also, there are some bacteria and molds which thrive in quite acidic environments (although few of them are pathogens). Oxygen is even worse, as botulinum is anaerobic and very dangerous. Also, once you open the canned food, it can get contaminated again.

Time and temperature are quite good, but they are no guarantee for no food poisoning. First, processing errors are common. Second, you can't sterilize the food in a normal pot, and the remaining bacteria resume multiplying even before it's cooled off enough to eat. And, if it was contaminated before the cooking, the pathogens can have produced temperature stable toxins before you cooked the food.

Moisture is probably the only factor which can produce completely safe food. Most dehydrated food is not 100% safe. Beef jerky, cured hams, dehydrated fruit, nuts and similar can easily grow toxic mold during improper storage. Depending on how much water was removed in the preservation process and where you live, the kitchen shelf can turn out to be "improper storage". Flours are quite safe too, but you have to cook them, and the cooked product is again not guaranteed to be safe.

The only foods which will be completely safe will be the ones which never had any moisture to begin with, and will remain bactericidal if they acquire some moisture from the air. So sugar (either granulated, or hard candy),salt and pure oil can be declared safe from pathogens, but not from some kind of factory mishap where toxins can have contaminated the sugar and oil. A protein powder may fall in this category, I'm not completely sure how little moisture would be sufficient for a mold to grow on it.

And don't forget that you can infect yourself with digestive tract pathogens by handling the food with contaminated utensils or fingers, even if they don't get the chance to build a colony in the food. You could in principle hold your dining room clean to operation room standards, but people get infections in operation rooms too.

Nutrition is off topic for this site, so I won't discuss the wisdom of eating nothing but sugar, oil, salt and boiled water in order to eat guaranteed pathogen free food. For me personally, the trade off is absolutely not worth it.

Picture: Spiritus is a Polish vodka that is 98% alcohol by volume. I should think it is as sterile as it is possible to get.

Foods that are very high concentration chemicals are typically poor habitats for bacteria and moulds. Items which are high sugar, high salt, or high alcohol would typically be safe. You probably have pure sugar and salt in the house but other high sugar foods would include honey, syrups, treacle and some jams.

It is possible for these foods to become damp and thus bacteria or mould may grow on the dampness. A jar of jam may develop a damp patch on its surface that is slightly sugary but not too sugary and thus a great habitat for many bugs.

The safest thing I can think of is strong alcohols such as vodka, whiskey, rum, brandy, etc. These all have sufficient alcohol to keep themselves, and anything else they contact, sterile. Even wine and beers are sufficient strong to keep sterile.