In the comments:
And yes, species concepts are much more fuzzy in many cases. Were mice to hold their own Olympics, they might well have learned (if slightly furry) discussions about whether musculus/domesticus/castaneus should compete in the same events, and if so, which events molossinus or other hybrid individuals should compete in. As humans, we dodge that bullet by having no closely enough related species to confuse the issue. The difference between us and a chimp is well defined. If Neanderthals were still around, that would be a different matter.
What happens is a nation (e.g., China?) reconstructs a Neandertal individual from the sequence in the public domain as well as segments from living human beings. Do they get to compete as power-lifters? This might seem like a crazy question, but I’m not totally unconvinced that it will be just academic within our lifetime. Genetic modification is likely to become ubiquitous within a generation.
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