I should have mentioned in my post that I have an applied math masters and a solid amount of analysis and linear algebra with some group theory, set theory, and a smattering of topology (although no algebraic topology). So, I'm not coming to this with nothing, although I don't have the very deep well of abstract algebra training that a pure mathematician coming to category theory would have.

Although, it feels like category theory _ought_ to be approachable without all those years of advanced training in those other areas of math. Set theory is, up to a point. But maybe that isn't true and you're restricted to trivial examples unless you know groups and rings and fields etc.?