2) Your immune system's memory response and capacity for leniency towards non-self antigens.
Here's a nice, comprehensive look that contrasts cleanliness versus pollutants:
D. Diaz-Sanchez Pollution and the immune response: atopic diseases – are we too dirty or too clean?
I can quickly summarize some of the basics behind the theory (antigen is basically anything that's not part of your body - it can be a virus, a bacteria, or just chemicals it doesn't recognize):
Your immune system has both a nominal response and a memory response. The initial response is made by the Innate immune system, and is responsible for allergies (Mast Cells contain large amounts of Histamine - the primary agent in allergic reactions). Whether or not your immune system responds a little bit, a lot, or just the right amount depends on previous exposures to antigens. Your Innate immune system can learn that some compounds (like pollen) don't require a large response, but only if it's been consistently exposed to pollen before. This is part of the reason why "Exposure Therapy" for allergies can yield success. It's basically repeated exposure to the allergen at higher and higher doses until the immune system stops overreacting.
The Memory Response is one of the most effective ways your body fights off infections, and it's the reason why vaccines are so effective. Once you are exposed to an antigen, your Adaptive immune system retains some white blood cells in the lymphoid tissues. If your body encounters the same antigen again (Chickenpox), it already has an extremely effective responder ready to undergo mitosis to quell the invasion. As you age, your immunological memory expands, to the point that removing the Thymus (the primary source of new T-cells - which are the basis for the Memory Response) becomes less and less of an issue as you age. After about the age of 35-40, the removal of the Thymus barely affects the immune response at all since the person is more or less encountering what they've already seen.
Between the two the argument for the "Living too cleanly" is basically thus:
If you do not encounter a lot of antigens, like in a sterile environment, your body's immune system does not correctly calibrate itself and can overreact when it is exposed to unfamiliar antigens. Also, there's the possibility that if you were to spend several decades away from sources of antigens, that your Memory Response library would be severely lacking - resulting in more severe illnesses which take more of a toll on an elderly person than young person.
I'm not aware of any threshold of cleanliness that there's been agreement upon deciding which level of cleanliness is fine or not. I would think that as long as you get outside often, socialize occasionally, and keep your living areas relatively clutter free you're good. Obviously do not do something like refuse to clean food prep areas under the delusion that it will only make your immune system stronger. It might do that until you catch Salmonella or something much worse, then you're in the hospital paying a few thousand dollars to vomit into a fancy bucket.