Identity, like beauty, fun, and spiciness, is[1] something that's built on physics, not requiring a fundamental property, just as asking how much spiciness an electron has is futile.
[1] Well, presuming it actually does exist as something other than confusion, which I'm not currently arguing, though I'm sympathetic to the notion.
Beauty has physical structure on a couple levels. You can either talk about certain synapses lighting up (or whatever happens in the brain when someone experiences beauty) or you can talk about facial symmetry and 1.618.
Fun is an extremely vague notion, I'm not sure what it means or if it even has a consistent set of synaptic patterns (or whatever), but I think that's probably because people don't use the term consistently (or are confused, etc., as you say).
I think the problem there is with the first half of that statement,
> Just because physics doesn't have a notion of identity
I inferred that the intended meaning was "Just because the field of physics has no notion of identity". Obviously in philosophical and sociological circles there is absolutely a concept of identity.
How is that not exactly what that means?