I'm not so much talking about the legal definitions, as about the basic intuitions that form the framework for the moral reasoning that goes into determining behaviour and then the formal laws and systems that govern them.
It's one of the priors that someone with a non magical upbringing may never consider, that the basic foundation of moral reasoning is different for pureblood wizards.
That other sapient beings have weight as moral actors is pretty basic, and if pure bloods were to instead use a different intuition as the starting point for moral construction, then Harry has a very substantial amount more work to do.
n.b., I have to admit that I was rather disappointed by their being a physical basis for magical ability that proved Harry was right and the pureblood faction wrong. I think it would make a far more interesting setting if the pure bloods were actually factually correct but still morally wrong. Just as interesting would be there being no physical basis for magical ability, and it simply being an example of large scale magic such as the taboo or the cure on the DADA job, the equivalent of a curse or blessing on a family line.
The discussion of snake's sentience reminded me of an argument I once made about the nature of pureblood discrimination against Muggles, which I'll reproduce here:
Consider how we, as humans, justify our definitions of personhood. Why do we say that chimps, for example, are not people? Essentially, we come up with a list of features which we have, and things which aren’t people don’t have, like talking, tool use, etc. and then say everything which looks very similar to something which has those features is a person (why, for example, we consider a severely mentally retarded person a person).
In the Wizarding World, manufacturing a facsimile of sentience – talking, etc. is trivial. Even a very poor family can purchase multiple such objects as a child’s toy (Magical Chessmen). They would reject that these object are people, they’re simply toys, not truly free willed, despite resembling that strongly. When it comes down to it, the only difference between real people and all these simulacra seems to be the ability for autonomous magic use – so this becomes the criteria for person-hood.
For wizards, form is not a determinant of nature, thanks to the various transmutations and shapeshifting that is possible, this means that something looking similar to a person cannot be assumed to have the characteristics of a person, so the familiarity based extension I mention above that we have doesn’t apply.
All in all, by this rather natural definition, Muggles aren’t people. All they are is clever simulacra, with no greater moral significance than a child’s toy.
Move back to the chimp analogy. A chimp can do many things a person can do, but falls short on the key criteria. Despite this it’s being suggested that human-chimp hybrids may be genetically viable. It’s quite possible such a hybrid would then meet the criteria for personhood by our definition. Would you approve of people breeding with chimps? Or accept chimp-human hybrids as full members of society without reservation?