Speaking as a Native from the East, it's not so much sensitivity as it is an annoyance and sometimes inappropriate. Oftentimes when people find out you're indigenous, you become the Spokesperson for all things Native America for them, and it becomes exhausting. I spent an hour on standby at a recreation center during an EMT shift the other day fielding questions for an older gentleman waiting for the pool. After the first half-hour, it became intrusive and inappropriate to ask a complete stranger (and I would have requested he stop asking questions, but I didn't want to be mean to this older gentleman, although it was in my right to request he stop asking me about Lincoln's massacre in 1862).
There's a time and place to ask questions, but my family's experience has been that people feel obliged to answers to all things indigenous, nevermind the fact that there are 500+ tribes out there and you may have just met them. You're treated like a unicorn in your own homeland and it's ridiculous.