I’ve always figured this has a lot to do with the model and/or function of the particular droid. A translator like C-3PO or an onboard mechanic like R2-D2 or BB-8 is going to be interacting a lot with sentient organics, so they’ve probably got much beefier AI to the point where they’re considered “people”. Other ones with more specialized functions like Gonk droids or Mouse droids probably don’t have nearly as much computing power, and thus don’t have that kind of self awareness.