Generally, using a GPS on a plane should do no harm to the plane or the security on board, since the GPS device does only receive data and not send anything itself. Because it doesn’t send, it has no way of interfering with instruments in the cockpit.
Secondly, GPS is also used up front in cockpits, so it is a save and common technology used in aviation every day. Many airline pilots use their own devices in the cockpit or allow passengers they know to place theirs in the cockpit. However, some airlines prohibit GPS on board of their planes.
Fun fact: Commerce Department regulations on self-guided missile technology keep GPS receivers from reporting speeds greater than 999 MPH, or altitudes in excess of 60,000 feet. As this is higher than Mount Everest, and nearly 20,000 feet higher than airline cruise altitudes, you won’t see it on your typical commute.