So it seems like exposure to microbial loads from farm animals help prevent allergies. But humans have not always kept lifestock - what kind of microbial exposure do pre-agrarian peoples receive?

Preparing and eating all food, for one.

There's a correlation between old school values and avoiding new school problems.

I have saved several exgfs from lifelong headaches and migraines, some no longer having to take their controlled quantity strong prescription migraine pills. I had them substantially up their salt intake. But they'll still worry that too much beef is going to kill me, because the same doctor that couldn't help them with their headaches says so.

Meh. Old school values include a lot of superstition, abuse, and destructive practices. If we want the benefit from the good we need to be able to systematically separate the wheat from the chaff.

Electronics and tightly sealed houses, both of which the Amish might avoid, together allow for a lot more formaldehyde build up indoors. My pet theory (with no proven evidence except my own two eyes, as someone possibly affected by formaldehyde, which means the details are just guesswork right now) is that formaldehyde indoors is responsible for the increase in reported allergies, poor vision (glasses), asthma, ADHD, and possibly increases in divorce rates or staying single - by which I mean that it can cause irritability.

I figure it is the primary cause of road rage, that it can possibly bind to and release microparticulate of metals like iron and aluminum, that it can store itself not just as a solid at room temperature but also in the rubber parts of a scooter while it charges or silicone or foam parts of a CPAP as you breathe in and out (you naturally produce formaldehyde, but increased presence in your exhaled breath has been associated with cancer, for example).

It also causes insomnia and can cause very low humidity in an enclosed space, which might both increase static shocks but also possibly break electronics when combined with its effect on certain metals mentioned earlier.

I’ve an even crazier pet theory that in the presence of other VOCs and sunlight, formaldehyde can multiply, but I don’t have anything to back that up. Formaldehyde with CO2 and UVA can react to become ozone, but ozone with UVA and other VOCs can become formaldehyde. As a result, on a particularly sunny day, I think even outdoor formaldehyde levels can rise and cause the day to feel even warmer than it otherwise should, and that it’s the formaldehyde that can then cause more inattentive accidents.

I’ve another theory that if you take something on to a train with micro metal particulate offgassing and formaldehyde, that it will bind itself to the heat of the wheels over the tracks and be released along with microparticulate from the metal rails every time the train runs by.

I could give more evidence of why this might be so, such as increased rates of emergency repairs of train tracks in my area, Toronto, and a study from 2017 that says Torontos subways have the most metal particulate in NA, but since it’s just speculation right now, take everything I said with a grain of salt, please.

I should add that burning natural gas indoors without appropriate airflow is a wonderful way to introduce a lot of formaldehyde to your living quarters over the years. If I could ban all forms of combustion indoors, I would, I really would.

The actual answer is pretty much in the article and what you would expect:

"The prevalence of allergic sensitization - the development of antibodies to allergens and the first step to developing an allergy - was six times higher in the Hutterites. The researchers first ruled out a genetic cause; in fact, an analysis showed that the Amish and Hutterite children were remarkably similar in their ancestral roots. Instead, the main difference between these two populations seemed to be the amount of exposure as young children to farm animals or barns.

“The Hutterite kids and pregnant moms don’t go into the animal barns. Kids aren’t really exposed to the animal barns until they’re like 12 or so, when they start learning how to do the work on the farm,” Ober said. “The Amish kids are in and out of the cow barns all day long from an early age.”

When analyzing samples of Amish and Hutterite house dust, they found a microbial load almost seven times higher in Amish homes. Later experiments showed that the airways of mice that inhaled Amish dust had dramatically reduced asthmalike symptoms when exposed to allergens. Mice that inhaled Hutterite dust did not receive the same benefit."

Good points. And it probably isn’t formaldehyde. The only thing I’ll add is that formaldehyde can inhibit or kill bacteria. And I also recently learned the hard way that limonene or other terpenes (from fruits or cleaning products or air fresheners for example) can react with ozone and produce formaldehyde even in the absence of combustion. And I’ve a strong opinion now that science and society ignores the dangers of formaldehyde and VOCs about as much as we used to ignore germs and other things we can’t usually see. Until heat pumps with fresh air exchanges are considered standard or specified by housing code, we will probably always have to deal with VOCs as we don’t have an accurate way to measure them and identity their sources except in industrial contexts. Saying this because while an open window is the cheapest way to get fresh air, it often isn’t the temperature or humidity we expect.

Amish would do a lot more burning of wood, kerosene, and other things indoors than the average population, wouldn't they?

We readily metabolize small amounts of formaldehyde (it's a step in normal metabolic pathways).