Logic gates from everyday materials
It is possible to build a Turing machine with "Lego" elements without any electric components, only with pneumatic transmission of energy. The guys who did this used some logic gates with pneumatic but this was the very easy part. The underlying automaton was way harder to build. (webpage in French. The other Turing machines in Legos use electronic devices which is very much like cheating)

Moreover I know you can build logic gates using only Lego elements and that may be more relevant.

So mechanics as well as pneumatics are enough to build logic gates.