The disc shape is a preferred form for galaxies due to angular momentum, and the axis of rotation indicates a locally preferred orientation for the angular momentum vector. Why do galaxies in Hubble Ultra Deep Field appear to have random axes of rotation? What scaling laws are in effect here?
The galaxies in the Hubble ultra deep field are spread over a wide range of redshifts. For disk galaxies, z ranges from about 0.2-2 (Melody et al. 2007). As such they are separated by billions of light years.
Whilst there are reasons to suppose that there could be some coherence in rotation axis orientation on the scale of galaxy clusters (see for example here), this would be on scales below 10 million light years. There is therefore no reason to expect any alignment between galaxies in the UDF that are not part of a coherent structure.