For me, the clear answer is "Oh fuck no!" I need to come up with a response for the younger set. I've been struggling for a more toddler-appropriate phrase that expresses the sentiment "you are shit out of luck." So far, nothing seems quite satisfactory.
This page of monstrosities comes to us from the monstrosity that is the Chasing Fireflies company (I'm not even going to link to them). If you aren't familiar with CF, they seem to specialize in sparkle/fairy/princess of the something-about-that-outfit-seems-inappropriately-sexualized variety. But, at least I know if I need to buy LB a costume befitting a child prostitute in a 19th century bordello, CF will be there for me. Maybe they can get Brook Shields to design a Pretty Baby line of costumes.
Until LB is old enough to earn her own money and sneak out of the house with her party clothes in a bag she will not be dressing as "a Native American," "a Black," "a Jew," "a Chinese," or any other racial or ethnic group. Not surprisingly, CF seems to have missed the memo on the Urban Outfitters "Navaho" underpants controversy.
My family has a lot of pictures from back in the day of little kids in "Indian" costumes. One of my great uncles was a proud member of the Order of Red Men (there was a Red Men lodge in our old neighborhood in Baltimore), and he was also the direct descendent of an Iroquois (Haudenosaunee) woman. It's so interesting to think of this man who had lost the Haudenosaunee part of his cultural heritage and then embraced a white faux indian-ness. So if perfectly nice people dressed up as "Indians" as children and remained perfectly nice, and if people of indigenous heritage participated in fake "Indian" culture, then can it be so wrong? What if a white woman is invited to a South Asian wedding, is it racist for her to wear a sari? What if a black man is invited to a Scottish wedding, is it racist for him to wear a kilt? [These examples are plucked from some of my favorite cultural commentators.]
To which I would reply: A) Try holding your breathe until your Navaho "best friend" offers you some sacred garments to wear as your Halloween costume.
B) For me, the question is do I want to make other people feel demeaned or disrespected over a costume, when there are an infinite number of alternatives that would not be demeaning or disrespectful. People have a wide range of opinions, and certainly there are people from all groups that wouldn't be offended by this sort of dressing up, but I wouldn't want to have to look someone in the eye who was offended and explain myself. And clearly cultural boundaries aren't absolute. We cross and mix and borrow constantly, but that borrowing should be a conscious choice, not the perception that another person or their culture is a thing that can be purchased and discarded.