Do airliners stall first at the wing tip?
They are designed to not stall at the tips first. Such a stall behavior would be highly problematic because it causes a pitch-up moment which exacerbates the stall. See the answers to this question how nasty stalls with swept wings can become.

FAR 25.203 describes the required stall characteristics:


  (a) It must be possible to produce and to correct roll and yaw by
  unreversed use of the aileron and rudder controls, up to the time the
  airplane is stalled. No abnormal nose-up pitching may occur. The
  longitudinal control force must be positive up to and throughout the
  stall. In addition, it must be possible to promptly prevent stalling
  and to recover from a stall by normal use of the controls.


Such a behavior is easiest to achieve when separation does not start at the wing tip. Earlier swept wing designs sometimes had trouble to achieve docile stall characteristics which led to the introduction of stick shakers. Today, changing the airfoil shape over span (aerodynamic washout) and wing twist (geometric washout) are combined to ensure that stall starts at the wing root.

Regarding washout: With high-lift devices employed, the low deflection angle of the ailerons on the outer wing results in a strong effective washout. Here it is important to extend the slats over the outer wing to enable it to function well above the local angle of attack. The picture of an A300-600 below should illustrate the point.

 

A300-600 in landing configuration (picture source)

But even in clean configuration some washout remains and allows the outer
wing to fly at a lower lift coefficient which ensures a decent stall margin. A photo of an airliner wing on the ground might be misleading: The lift forces in flight will twist the swept-back wing such that washout is increased.