why would species have anything whatsoever to do with this? Everyone deserves respect regardless, obviously.

IMO the ideal is to just leave things be if we're confident it won't be disturbed (this is both respectful and means we can use better methods to study it in the future), and if we're not confident then we extract things and preserve them in as respectful a manner as possible.
Don't disturb more than necessary, have people perform whatever rituals they feel are suitable, and if at all possible restore the site as close as possible to how it was (but making sure it won't degrade).