I don’t know about ANA tests in particular, but nuclear proteins in general tend to be highly conserved (I.e. similar across a wide range of species). This makes sense because the basics of DNA replication and RNA production are virtually identical across hundreds of millions of years of evolution. Wikipedia’s article on conserved sequences notes that many of them are the “proteins required for transcription and translation, which are assumed to have been conserved from the last universal common ancestor of all life”.