The magnetic field inside a long solenoid is uniform and directed along its axis, while the field outside it is essentially zero. When one solenoid is coaxial and nested inside another, the inner solenoid sits in a region where the outer solenoid's field is uniform (so net force is zero), and the outer solenoid's windings sit in the field of the inner solenoid, but by symmetry and Newton's third law considerations for this configuration, both net forces vanish.