U1A is a CMOS device so the current drawn into it's input pin will be extremely low, probably only a few nA. The Neon lamp is effectely open circuit until it has striking voltage across it so there is almost no load on the antenna input wire and it 'floats' at whatever voltage is around it. What you are seeing is diturbances in the electrical field around the antenna. Some of this will be radio pickup but most will be from interference from electrical loads being switched on or off and from atmospheric discharges (lightning flashes). Mobile phones transmit on much higher frequencies than these logic gates can switch so it's not suprising they don't operate it although you might find that a the flashing stops when an operating phone is nearby because it will induce DC offsets into the circuit which will to some degree stabilize the logic levels.
Incidentally, the neon will not work as protection as it is at the moment because any signal greater than the supply to the ICs will conduct current into them and destroy them will before the neon strike voltage is reached. You should consider much higher values for R1 and R2, at least 1M each to protect the ICs. You can also remove C2, R3 and R4 and connect the output of U2A to the transistor base through a 10K resistor to simplify the circuit.
Brian.