I think many people are coming at category theory with a feeling that it has interdisciplinary ramifications and offers a unifying lens on multiple topics. Specifically I think the topics that have all drawn me towards category theory in different ways are:

1. Philosophy and formal logic (and other structures that have surprising isomorphisms within math and science).
2. Functional programming, type theory, and lambda calculus (and how these represent a bridge between computer science and mathematics)
3. Knowledge graphs and other systems for modeling information (semantic triples, RDF, etc)