Should I add extra protection to 74HC4067
long wires act as antennas. ESD is one problem, EMC is another. Then there is lightning. The degree of protection really depends on the environment.
The ESD diodes on ics only provide a small amount of protection and are inadequate for wires that go out into the real world. Putting protection after the mux is useless.
For a commercial design, we determine the expected environment for our device and apply the appropriate standards that guide what level of protection is required. For a hobby project, we don't need to go to that length, but is good practice to follow.
We also need to specify what the expected signals are - frequency range, impedance voltage, current and so on as this guides us as to what techniques we can use for protection. Minimal protection would be a RC filter and maybe TVS diodes, varistors etc. As well, the type of wiring - shielded? etc.
As well, hardware is only part of the solution. Your software needs to filter adc values, debounce/filter digital inputs to ensure the rest of your code responds to valid inputs. The old maxim 'garbage in/garbage out' applies. None of this is particularly difficult (usually!) but if considered during the design phase makes the likelihood of a successful project much greater.
Or you can simply ignore all of this. If so you can expect the following:

noisy signals. Mobile phones might give random interference.
nearby lightning strikes might damage the circuitry
ESD might damage the circuitry
Induction from nearby mains wiring etc can couple and induce significant interference.
devices turning on an off inducing noise into your signals