How is A Tale of a Tub modern?

A Tale of a Tub by Jonathan Swift was written between 1694 and 1697 and first published in 1704. It is not a "modern" work in the sense of being a production of literary "modernism". There are two ways in which one can use the term "modern" in discussion of the book.
First, Swift himself refers frequently to "modern" authors and literary tastes. In Swift's usage, the "moderns," meaning authors of the late seventeenth century and early eighteenth century, are being contrasted with the "ancients": Graeco-Roman writers such as Homer, Virgil, Cicero, and Horace, and those later authors who imitate them and their virtues of rationality, symmetry, and adherence to nature. Swift was a strong proponent of the "ancients" in the controversies of the period between the "ancients" and the "moderns"—writers who wanted to radically innovate on the one hand and those who believed in imitation of ancient models on the other hand. Swift's "Battle of the Books," which was published as prolegomena to A Tale of a Tub, is a combative work that strongly supports William Temple (one of the ancients) in his controversy with Bentley (a modern) over the authenticity of the Letters of Phalaris. When Swift uses the word "modern," it is a strongly negative term used to condemn the moderns' stylistic excesses and slavish following of trends. In terms of genre, Swift looks back to classical models such as Aristophanes and Juvenal.
Another way in which one can think of the work as "modern" is that many of the features we may associate with "modernism," such as mixing fantasy with reality, intrusive self-reflexive narrators, and radical intertextuality were standard fare in the seventeenth century, less common in the late eighteenth and nineteenth centuries, and then revived by the modernists. In referring to this, it would be more precise to say that "modernism" attempted to revitalize the arts by a return to the seventeenth century (something T.S. Eliot says explicitly) rather than describing the seventeenth century as "modern."