Putnam's thought experiment can be easily tweaked to get around that problem: suppose that on Twin Earth cats are in fact very sophisticated cat-imitating robots.
That would be an even weirder version of Earth. Well, less weird because it wouldn't be a barren, waterless hellscape, but easier for my mind to paint.
A universe were cats were replaced with cat-imitating robots would be amazing for humans. Instead of the bronze age, we would hunt cats for their strong skeletons to use as tools and weapons. Should the skeletons be made instead of brittle epoxy of some kind, we would be able to study cat factories and bootstrap our mechanical knowledge. Should cats be self replicating with nano-machines, we would employ them as guard animals for crops bootstrapping agriculture; an artificial animal which cannot be eaten would have caused other animals to evolve not to mess with them. Should cats, somehow, manage to turn themselves edible after they die, we would still be able to look at their construction and know that they were not crafted by evolution; humanity would know that there was another race out there in the stars and that artificial life was possible. Twin-Eliezer could point to cats and say, "see, we can do this," and all of humanity would be able to agree and put huge sums of money into AI research.
And if they are cat-robots who are indeed made of bone instead of metal, who reproduce just like cats do, who have exactly the same chemical composition as cats, and evolved here on earth in the exact same way cats do... then they're just cats. The concept of identical-robot-cats is no different than the worthless concept of philosophical zombies. That's the whole point of the quote.
Well you could go for something much more subtle, like using sugar of the opposite handedness on the other 'Earth'. I don't think it really changes the argument much whether the distinction is subtle or not.
Thagard (2012) contains a nicely compact passage on thought experiments: