As far as I understand (I'm not a physicist), to be able to say that the universe is isotropic across space, you need a point of view that just doesn't exist. You cannot speak about an absolute synchronicity among events happening in locations scattered among an arbitrary subset of the set of all visible galaxies, and without that, you cannot abstract time out of the picture, which you'd need to do to speak about isotropicity across space.
I don't think that, in this regard, you can say much more than "the universe is not isotropic across space-time".
I don't think that, in this regard, you can say much more than "the universe is not isotropic across space-time".