Okay to mount Arduino to Styrene?

People use plastic enclosures all the time - a circuit in a PCB is usually
fairly robust to nearby static, its being touched by metal or fingers that are
charged up that causes issues since there can be significant capacitance
and thus energy behind (for instance) a human charged up to 2000V.

Touching a PCB trace to the surface of statically charged plastic can only
capture charge from the immediate vicinity and only if the voltage is high enough
to cause corona discharge at the sharp edges of the trace. The stored energy
is very small I think for this scenario due to the small area of insulating surface
involved.