The fundamental assumption of mathematics is that the number 1 is a meaningful concept, that the observation of distinct-ness between "different" objects isn't some flaw of human perception, that identity isn't absurd.

This isn't a trueism, as you say. It is a postulate.

Whether or not it is a fault of human perception to see one thing as unique to other things, no matter how similar, is unclear.
I mean, we are both people, similar in many ways, but we believe that we are not each-other, for a slew of reasons, all of which are based on our perception. So the assumption that our perceptions are a reliable way to describe us is woven in there.

I'm not saying it's a bad assumption, I'm saying it's undoubtedly an assumption, even if it is never shown to be false, it has no antecedent principles from which it is derived. I personally think the fact that it seems consistent in many ways (I keep perceiving to be me and not you all the time) is a strong reason to think it's not a bad assumption, but that just shifts the un-derivable onto my appreciation of consistency, which is ultimately a part of my perception, and now it's clearly circular.

All fields start with fundamental postulates, which, by definition, are not provable. Their worth is in their utility (change your pants, wuf).