Feynman’s objection is nonsense for the same reason that the Michaelson-Moreley experiment was a null test. The mean speed of the vacuum particles is the same in all directions, regardless of your frame of reference, because space and time in all frames of reference are defined by the presence of those vacuum particles. That does not mean there is no absolute frame of reference. It's just that the laws of physics work equally well in whatever frame we choose.
Presently, our best hope of discovering an absolute frame may be the foamy structure of the little bit of the cosmos that we can detect with out most powerful astronomical instruments. Logically, we should expect the foam to be isotropic; the mean shape of the voids should be the same, regardless of the direction in which they are measured. As Tom has astutely pointed out, it makes no sense that the voids should appear elongated in the radial direction as seen from Earth.
If we choose a frame which is moving relative to the foam, relativity will flatten the voids in the direction of the motion between our reference frame and the absolute reference frame. This should not bother us in the least; it's just an arbitrary point of view.
