Neanderthals Genetically Almost Identical to Modern Humans

From Yahoo News:
Researchers have sequenced DNA from the leg bone of a Neanderthal man who died 38,000 years ago and said on Wednesday it shows the Neanderthals are truly distant relatives of modern humans who interbred rarely, if at all, with our own immediate ancestors.

[…] The researchers reported their findings jointly in the journals Nature and Science.

[…] Neanderthals and modern humans are both descended from Homo erectus, which left Africa and spread around the world about 1.5 million years ago.

Neanderthals lived in Europe and the Middle East until about 30,000 years ago. Cro-Magnon people, the ancestors of modern humans, started a second wave of migration out of Africa about 10,000 years earlier.

One huge question is how closely they interacted. Paabo's and Rubin's genetic analysis both suggest there was little sexual contact, at least according to the genes from this one male found at the back of a cave in Croatia.

[…] They said the Neanderthal sequences are 99.95 percent identical to human DNA sequences. This compares to about a 98 percent similarity between humans and chimpanzees, who split from a common ancestor 6 million to 7 million years ago.

As a scientist and a Christian, I have never found a real intellectual problem between organic evolutionary theory (as opposed to “popular evolution”) and the historic, orthodox Christian faith. My question about this discovery is, at 99.95% DNA similarity, how long before they start demanding we clone Neanderthal embryos for stem cells?

For that matter, assuming we could get intact DNA, how long before we start growing them as slaves?