tl/dr:
In families who use hand dishwashing, allergic diseases in children are less common than in children from families who use machine dishwashing. We speculate that a less-efficient dishwashing method may induce tolerance via increased microbial exposure.
Studies are never able to prove causation. Phenomena in the real world are very rarely so simple as to have one trigger, often there are multiple involved.
Very often mechanisms are so complex, or simply hard to detect that it is only feasible to look at biomarkers and not the actual cause.
https://pubmed.ncbi.nlm.nih.gov/25713281/
tl/dr: In families who use hand dishwashing, allergic diseases in children are less common than in children from families who use machine dishwashing. We speculate that a less-efficient dishwashing method may induce tolerance via increased microbial exposure.