I don't think the ancestors of the spirit guardian barbarian are undead, they are just looking down from Ysgard (or wherever) and intervening.
Yeah, the soul of an ancestor properly residing in the afterlife and occasionally looking in on his descendants is not an undead. It's more of a Outsider, and could be properly represented as one depending on the alignment of the ancestor. D&D doesn't really do animism well, despite it touching on those mythologies from time to time. So it doesn't really have a collective category for Spirits outside support from third parties.
The OP's conception of Undead is partially inspired by Late Medieval Catholicism. The ghost of someone is not actually that persons spirit returned from the afterlife or doomed to wander the Earth. The ghost of someone is an evil spirit in the form of a dead person with the purpose of tormenting and misleading the living. When exorcising a ghost, you are not actually exorcising the soul of a person, but the evil spirit that has assumed that person's appearance. This conception precludes there being anything like good undead, since regardless of whom the spirit appears to be, it's not actually got the motives that person would have. In medieval Catholicism, this would for example extend also to the idea of vampirism. The vampire was not the person who you knew in life, but an evil spirit inhabiting and defiling the body of that person, perhaps pretending to be that person to gain unwarranted sympathy, but in fact being a blasphemy against that person had they been good in life.
This conception is not mutually exclusive with the idea of ancestor spirits or other helpful spirits, but it does mean that undead are categorically different from ancestor spirits.
It is also slightly different from my campaigns conception of undead, though in my game there isn't really anything like 'good' undead either. Ancestor spirits are just that, ancestor spirits and not undead. Zombies and skeletons are just evil spirits (or really, perhaps even less than that automatons without real volition), and the soul, personality, or will of the person is not present - similar to the OP's conception. While ghosts really are the person they were in life, to be a ghost you must be either evil or at minimum temporarily insane as a result of a traumatic death. While there are ghosts that aren't fully malevolent, there are no ghosts that aren't dangerous and no good person would want anything for a ghost but it to be removed from the world and properly laid to rest. For example, a ghost of a child (typically a Poltergeist in my game) is more mischievous than malevolent, but they are in great pain, are effectively trapped in a hallucination, and even more so than a normal child are not fully aware of the consequences of their actions. No good hearted person would want anything but for them to be laid to rest, and binding a ghost into your service in both inherently cruel and heartless, and extraordinarily dangerous.
