Arduino gets false triggers due to compressor switching on/off?
This is almost certainly noise, probably due to several design problems:

High impedance.  A passively pulled up signal has the impedance of the pullup in the quiescient state.  In a noisy environment, this pullup needs to be low, or passively floating lines avoided altogether.

No shielding.

Bad overall system grounding strategy.  Since you mentioned "arduino", possibly even no overall system grounding strategy.

Bad firmware.  Short glitches on mechanically switched lines should be expected.