We know that the CMB is isotropic when viewed outside of the spinning and revolving earth.
As pointed out in Edgar Bonet's comment, this isn't true.
Is it homogeneous?
Realistic cosmological models describe it as approximately, but not exactly, homogeneous. Homogeneity and isotropy can't be perfect, since the universe does have structure.
Can we relate the CMB to an inertial frame in the Newtonian sense (in which space and time are homogeneous and isotropic)?
You're mixing up a lot of unrelated ideas here. Inertial frames in GR are local, and spacetime is locally homogeneous and isotropic in any such frame. At any point in spacetime, the CMB can be used to define an inertial frame. Spacetime is locally homogeneous and isotropic in that frame. Spacetime is also locally homogeneous and isotropic in every other inertial frame, including frames in which the CMB is not isotropic. Anisotropy of the stuff that occupies space doesn't imply anisotropy of space itself.
Or can it just provide an idea to build upon a new theory in which global (privileged) inertial frames exist?
No, you can't have global inertial frames (because an inertial frame is a free-falling frame, and, e.g., a free-falling frame in China doesn't correspond to a free-falling frame in America). No, it doesn't have anything to do with a privileged frame, because the existence of some stuff occupying space doesn't imply a privileged frame. A privileged frame would be one in which the form of the laws of physics was different. No, it doesn't imply the need for a new theory.