I think it's extremely likely that humans are going to have a very hard time in the near future coming to terms with the fact that we are what are "in" our brains, and that our brains are basically just biological computers whose inputs, outputs, and how it converts the two, are very much a part of the natural universe and can be explained. And once we can explain it, we'll be able to predict it and thereby control it.

I know what you're asking and the point you're trying to make, and I totally agree that it's an interesting problem. Perhaps one method is that non-humans will get rights when they evolve to the point to create their own rights and the means with which to stop other things from trampling on the rights they have assigned themselves.