Are oscillators always non linear?
A practical oscillator has to be designed taking into account component tolerances.

In your example the ratio of RG to RF needs to be such that the gain round the loop is unity.

Because of the tolerance in RG, RF and the capacitors there has to be some extra gain designed in so that in the worst case the gain is at least unity.

In the typical case this means the gain will be greater than unity so the oscillations will keep building up until one of the amplifiers saturates, that is becomes non-linear, and the amplitude stabilizes. Since one of the amplifiers is saturating its output will not be a sinewave.

In your example saturation provides the amplitude stabilization but other techniques can be used that produce less distortion.

An old technique is to use a thermal device that varies its characteristics with the amplitude of the oscillation and in so doing alters the loop gain to stabilize the oscillations.  The first product from Hewlett Packard in 1939, The HP200, used an incandescent lamp as the control element.  Thermistors have been used in a similar fashion.

Electronic means can also be used such as incorporating an Automatic Gain Control (AGC) in the loop.