I have to agree, to a point, with Robert Handy.  As I
 have stated before, I would give my first born child for
 the opportunity to work in a Native American museum
 (yes, my son knows this).  But I have also stated that
 all other things being equal (training, experience, etc.)
 I know a Native American would be chosen over me.

This doesn't surprise or upset me.  I know a Native
 American, despite where he or she was raised, is going
 to connect spiritually and emotionally with a Native
American collection in a way I never can.  Others will
argue this with me and I know I am not explaining this
 very well, but to do so would mean a much, much,
longer posting.

Now, having said all this, I must state that I will continue to
 apply to every Native american museum that has an opening.
 I believe there is a museum out there that will not only see
 my qualifications but will also recognize my respect for
 Native American cultures, my willingness to learn from those
 who did grow up in the cultures, and my commitment to
present a true picture of those cultures to others.  All of
which is a little hard to confer in a resume and one short
 interview.

The point to all this rambling?  Keep applying to museums
outside your ethnicity, but don't be surprised if those powers
in charge don't alway recognize your abilities.