Think of it not in terms of “separate but equal” but more like, “if there were no Special Olympics (or something like it), the disabled couldn’t compete at all.” SbE addressed an inconsequential difference, making more of it than it was worth. But the differences between the abled and the disabled are not inconsequential, which is why wheelchair ramps are commonplace.
No, it is not separate but equal. It is not trying to be equal. Separate, but equal would be if there was a separate Olympics for Asians for instance. If they were not allowed in the regular Olympics.
@JLeslie No, I actually helped out at a Special Olympics event once. I saw it as a sort of parallel to the more commonplace track meet. I suspect that, had SO not arisen, there would be something similar in its place.
Separate but equal has way too much negative baggage to be attached to the Special Olympics. The Special Olympics is making no attempt to suggest its participants are equal to anyone else. It is instead about the aphorism, “Be all that you can be.”
You are thinking of publicly funded activities, as opposed to private donations. The rules that refer to participation are valid with a private entity.