It is possible that Democritus held views similar to those of David Hilbert with respect to Platonic ideals, but it is unlikely to be the sole reason that Plato called for the burning of all of Democritus' books?
Democritus was a pre-Socratic philosopher who lived in ancient Greece and is known for his development of the atomic theory of matter. While Democritus did not explicitly reject Platonic ideals, he did have a more materialist view of the world than Plato. Democritus believed that everything in the universe was composed of atoms and that the properties of matter could be explained in terms of the motions and interactions of these atoms.
Plato, on the other hand, believed in the existence of a realm of abstract, eternal forms or ideas that transcended the material world. He saw the pursuit of knowledge as a process of gradually coming to understand these forms and their relationships to one another.
It is possible that Plato viewed Democritus' materialist philosophy as a threat to his own views, which could have been a factor in his call for the burning of Democritus' books. However, it is also likely that other factors, such as political or personal disagreements, played a role in Plato's condemnation of Democritus.