The hygiene hypothesis
For some reason I hold the opinion that the immune system needs to be kept busy so it wont get weak
In scientific terms, this is known as the hygiene hypothesis. It was proposed in 1989 by Strachan and is about whether people who have been exposed to a lower amount of pathogens in their childhood are more likely to develop autoimmune or hypersensitivity (allergy) disorders later in life. Strachan actually didn't propose it in the context of hygiene, but in the context of families having less children and thus children being exposed to their siblings' infections less often, though. He found that children with fewer siblings had a higher incidence of asthma and hayfever and came up with the hypothesis to explain his observation. The name has stuck, though.
Is it true? Possibly.
Chromic inflammatory diseases are in fact more prevalent in the so-called developed world. As Ghana got richer and presumably 'cleaner', the rates of allergies and asthma increased.
The role of vaccinations
letting your kids get low-risk childhood sicknesses like mumps, rubella or chickenpox is "training" their immune systems
Basically, no, even despite the hygiene hypothesis.
First of all, whether these are not low-risk diseases is in fact debatable, but outside the scope of this question, I think. Mumps and measles can end in encephalitis. Since you can not guarantee that every child who isn't vaccinated will get the disease 'naturally', not vaccinating compromises herd immunity and can lead to the more vulnerable members of society (small children, immunocompromised patients, pregnant women) being exposed, which can lead to severe consequences.
The mechanism by which all of this works is a lot more complicated than that the immune system needs to be kept busy, though. It depends on what the infections are, when they are, and what kind of immune response they raise.
Scientists have tried to determine which pathogens play a role in the hygiene hypothesis, and the result is now called the old friends hypothesis. From the summary of the 99th Dahlem Conference on Infection, Inflammation and Chronic Inflammatory Disorders:
- The most relevant organisms are those that co-evolved with mammals, and already accompanied early hominids in the Paleolithic.
- More recently evolved ‘childhood infections’ are not likely to have evolved this role, and recent epidemiology supports this contention.
Pathogens usually indicated in research are worm/parasite infections, and general exposure to bacteria from the environment. Household hygiene is likely to only play a small part in the process, while an larger part is played by letting children be exposed to things outside of an urban environment. Diseases we vaccinate against don't seem to play a role.