Can passenger movement in an airliner make it stall?
I used to teach sport parachuting, and we occasionally pranked the pilots by shifting the weight around.

A Cessna 206 set up for parachuting will have all but the pilot's seat removed, the jumpers sit on the floor. Everyone moves forward for takeoff and then sits back for the ride up. The instructor (me) sits on the floor where the co-pilot would normally be, facing aft, everyone else faces forward. I would wait until the plane was trimmed for climb (and well above 1000 feet) and then motion the passengers to come forward a bit (the pilot cannot see this happen). He adjusts trim as usual, thinking nothing of it. Passengers come forward some more. Trim adjusted again. Eventually we have 5 people wearing 20kg packs all jammed up into the first 2 "rows" and the trim almost fully nose up. 

One signal, and 1/3 of the airplane's gross weight quickly moves almost 2 meters aft (in a 4 meter cabin), followed by a sharp pitch up in both the nose and the pilot's blood pressure. The stall alarm usually goes off too.

Mid-size tailgate aircraft used for jumping are regularly stalled by too many people on the tailgate for too long. The rule there is stay forward until it's your turn, then go aft and get out (if the buzzer goes, you get out NOW).

So it's possible to stall a small aircraft by moving the passengers around.

Scaling this up to airline sizes, we find that the passengers are a rather smaller percentage of the airplane's gross weight, and the presence of things like seats, bulkheads and galleys at the rear prevent 300 people from gathering rapidly at the back. The rather large hydraulically powered elevator also has substantial authority over the aircraft's attitude.

So no, a small group of passengers won't be stalling an airliner out of the sky no matter where they stand. Noticed by the pilots: possibly.