Is it surprising given that the existence of a preferred frame in the universe (from the cosmic microwave background), the cosmic rest frame, that there are no preferred observers? (Lorentz invariance in particular not being broken by this special frame.)
Should we expect any other measurement (besides the dipole in the CMB) that distinguishes observes that are traveling at different speeds with respect to each other?
Should we expect any other measurement (besides the dipole in the CMB) that distinguishes observes that are traveling at different speeds with respect to each other?
Sure. Pick any object you want, and consider the special set of frames in which that object is at rest. Observers traveling at different speeds with respect to the object are then distinguished from one another. This is precisely what you are doing when you select out the frames in which the CMB appears to be isotropic.
The fundamental postulate of special relativity does not say that all phenomena look the same in all reference frames (obviously), and conversely the fact that phenomena look different in different frames does not conflict with relativity. Instead, the point is that the laws of physics take the same form in every inertial frame, and that the predictions and observations of one observer can be related to the predictions and observations of any other via the relevant Lorentz transformation.
No, it should not be surprising. You are begging your own question by referring to the CMB frame as a 'preferred' frame. The point of SR is that all inertial frames are equivalent, in the sense that you can apply a common set of equations (the Lorenz transformations) to equate the values of physical properties in one frame to the values of the same properties in another frame, and the laws that govern the relationships between physical properties are not frame dependent.
As for the second part of your question, CMP dipole measurements allow you to determine how you are moving with relation to the CMB. That is no different, in principle, to a host of other measurements you might take to establish how you are moving with the relation to the Sun, or to Andromeda, or to a passing bus.
