Force on a current carrying loop in a non-uniform magnetic field

It is, of course, not true that there is always a force and a torque. There are usually equilibrium points where they vanish for a certain orientation of the magnetic moment (aka current loop). The torque on a magnetic moment in an external magnetic field (no matter if homogeneous or inhomogeneous) is $$vec T=vec mu times vec B$$ so if the magnetic moment is locally parallel (tangent) to the magnetic field, the torque vanishes. Similarly, the force on a magnetic moment in an inhomogeneous magnetic field is $$vec F=vec nabla (vec mu cdot vec B)$$ so if there is a point where the inner product $(vec mu cdot vec B)$ is locally constant, the force vanishes.

This situtation does not change in principle if the current loop has finite size (can't just be represented by a singular magnetic moment), the derivation, that there could be equilibrium configurations, only gets more complicated. And it is not necessary to consider this case, because the situation for the point-like magnetic moment already constitutes a counter example to the attribute "always".

However, these equilibrium configurations usually form only a finite set of points. So it is correct to say that almost always a magnetic moment (and hence, a current loop) experiences a force and a torque in an inhomogeneous magnetic field.