Which would mean integers are baked in, rationals too, but non-constructible reals (essentially all reals, given any degree of approximation) are a useful abstraction but don't actually exist in any way.
Reals are not real.
(Roughly) Equivalently: There may be no perfect circles in nature.
For one thing, they're speculative: the current theories that give the most precise and accurate predictions within their respective domains of applicability are general relativity and quantum field theory. These theories are based on continuous space and time, and no attempt to base them on discretized space and time has been successful (AFAIU both QFT and GR rely on Lorentz invariance, which means there's no absolute rest frame, hence no absolute unit of time and space, but a discretized spacetime would require absolute unit values for space and time, hence an absolute rest frame).
Should we conclude then that the reals are real, because they're components of our best current physical theories? Maybe, maybe not: these are features of our current best models, but we don't know, and possibly will never know, the ultimate nature of physical space and time.
For another thing, even if space and time are fundamentally discrete, there's still no doubt that the mathematical theories based on real numbers are effective in making predictions, and we would still like to use them. That's means they should have some logical foundation which can guarantee that reasoning using them is correct.
But this claim is nowhere made in the comment? Like clearly the transfinite ordinals aren't real, but no one would say that implies they aren't a very useful mathematical idea (and also just interesting in and of themselves).
"It seems wrong to me to base mathematical ontology on speculative theories about the nature of physical space and time."