I think that there are softer versions of Platonism (which in other contexts would not be considered Platonism at all, but are closer to Platonism that Smolin's idea) that are somewhat consistent with naturalism. The softer version is that there appear to be mathematical objects with independent existence, even though there is no a priori philosophical reason to believe in their independent existence, and there are indeed reasons to doubt it (e.g. non-standard models of not only the reals, but also the natural numbers).

One reason I find it hard to reject Platonism entirely is that the main alternative in the philosophy of mathematics, Formalism, looks to me like a kind of Platonism. This is because formalism replaces belief in the independent existence of mathematical objects (real numbers, integers) with belief in the independent existence of meta-mathematical objects (theorems, proofs) which most formalists conceive of in mathematical terms.

Ultimately I think that there is no a priori limit that we can place on how science is going to pan out, and how this will affect our philosophy. E.g. I find the idea of multiple universes distasteful and nonsensical (e.g. If everything possible happens, then how can we interpret probabilities? Why do we live in a universe where macro observations are consistent with applying the law of large numbers to quantum randomness? I can't think of any anthropic/observer based principle that would enforce this) but I can't yet rule out that that's really how things are.