We are not accelerating within our own reference frame. We are at rest with regards to the CMB, which any other observer will observe from their FoR (Every galaxy is the center of its own OU with expansion moving outwards.)
Distant galaxies can be receeding from us >c. As to them we would also appear to be moving >c. There are no prerferential reference frames though - so while we can observe expansion >c this is not "acceleration" through space so GR still holds up.
Hopefully we will get some knowledgeable posters here as this is something I would like to explore a little bit further.