Thinking about it directly again has given me a slightly different perspective, though. Maybe this resemblance of extremely general structures to human mental structures just relates to facility of expression, and isn't necessarily moving us further from objectivity—it's just easier for us to express our concepts as parameterizations of a structure that resembles the abstract structure of human concepts. The different parameterizations we can supply constitute all possible human concepts—but the important thing is that some of those concepts will be valid descriptions of objective phenomena, and those are the ones we attempt to supply.
No. First of all, it resembles a structure human minds can hold, not most structures human minds invent. It took work to get to category theory, thousands of years of it. Also, if the human mind didn't contain some small kernel of ability to accurately generalize from the real world, it wouldn't function as a living creature's mind, so we can trust, in the sense of a proof of existence, that evolution built us to reason correctly sometimes.