toilet, lavatory, mingle with
廁 centers on a place for bodily waste: a toilet or lavatory. The sense 'mingle with' is a distinct, less common meaning that does not clearly connect to the toilet idea.
廁 combines 广 (building enclosure) with 則, which likely contributes sound. The exact historical development is uncertain, but the structure suggests a building-related meaning.
Under a roof 广, there is a rule 則 about where to go: 廁 is the toilet, a place with strict rules for cleanliness.
For シ, imagine a shy person using the toilet: shy -> シ, and they need privacy in the 廁.