No specific interaction is documented for Arugula and Parsnip in the sourced chart. The compiled extension-backed companion table has no good or bad verdict for this exact pair.
That makes this a normal garden-planning decision. Put the crops together only if their mature size, watering needs, sun exposure, and harvest timing work in your bed. Keep family rotation in mind if they are related crops.
No companion-planting benefit or incompatibility is claimed here because no source row was found for this exact pair.
Spacing tip: Sow in bands rather than one mixed clump, then thin promptly so roots and leaves have room.
Sources
No extension-backed source row was found for this exact pair.