I'd describe category theory as the study of connected things. It turns out that many things are connected, and often the connections are exactly what makes something both interesting and complicated. Getting better at those sorts of problems is a concretely useful skill. And it's not just functional programming, where connections are functions between things. You can have things like orders, where a single connection exists between x and y iff x <= y. There's a nice connection between database schemas and categories too. I've found it useful in formalizing difficult problems.