Rosalind English asks: If science was able to resurrect Neanderthals, would they have human rights?
I think yes, due to the likely way in which such a resurrection would come about.
Consider the way in which gene enhancement techniques will work, when scientists perfect their methods. They will fertilise an egg by means of IVF, and then test the DNA of the petri-dish embryo for whatever it is they are concerned about. They will isolate undesirable genes (such as, a predilection for cancer, green eyes, low IQ, &ct) and replace them with desirable genes (cancer resilience, blue eyes, high IQ, lizard skin, &ct). Then they will put the resulting embryo back into a womb, in the expectation a baby will grow as a result. Such a child (hereafter referred to as an Enhanced baby) will undoubtedly be considered to have human rights… even if a portion of its DNA is from elsewhere in nature.
Now, a future Doctor Frankenstein (or for greater literary accuracy, Doctor Moreau) will probably create a Neanderthal baby by means of similar IVF techniques. They will take the sequenced DNA from the Neanderthal, stick it into an empty embryo, and implant it into a host mother. The child will grow and be born like homo sapien babies, and also the Enhanced babies described above.
Genetically speaking, both the Enhanced baby and the Neanderthal baby will have some strictly homo sapien DNA. In the Enhanced case, that’s because the original DNA was human. In the Neanderthal case, it turns out that they bred with homo sapiens in pre-history, so their DNA and ours share similarities above that of other simian species. The mixing of Neanderthal and homo sapien genes at the dawn of the anthropocene is similar to the artificial methods being developed now, that will one day create Enhanced babies.
In the case of both Enhanced and Neanderthal people, there will of course be some uncommon genes. But that would probably not stop them breeding successfully with regular humans. So it would not be said that they are an entirely different species (we certainly would not want to make such a distinction in the case of Enhanced babies, whose parents would be undeniably homo sapien). And if we are not willing to classify either type of person as a different species, it is difficult to see how we could avoid saying that they are deserving of human rights. To do so would be a form of racism.