In your situation I think I would count on the strength of my own denominational traditions. If the speaker is a member of your own denomination (which you suggest but don't explicitly say) you don't want to suggest that your denomination's traditional music is less hers than yours, simply because her ancestors were resident on this continent longer than yours. Likewise if the "Native American Themes" are consistent with your denomination's message, do you perhaps demean them by suggesting that they would never be incorporated into your worship if the substitute pastor didn't have Indian ancestry ? and do you perhaps slight the strength and breadth of your denomination's message by suggesting that these "Native American Themes", even though they are consistent with your message and therefore implicit in it already, are somehow more hers than yours ? I don't necessarily know that I'd answer these questions either "yes" or "no" in your situation, but I'd think about them.
A list of federally recognized tribes is here.
P.S. in case it matters to anyone's evaluation of my opinions: I have no documented Indian ancestry. Those who believe in the existence of WASPs would probably classify me as one, though I don't think of myself in such terms.