I think there are several issues at play here that make this a complicated situation. A couple of questions might help -- what is the context for the costumes? Will they be putting on a play? Acting as tour guides? Simply wearing the costumes to be cute? Also, how elaborate have the costumes been in the past? Can you get away with simple things like jewelry? Finally, how old are the children?
If you decide to go with costumes that represent people you want to be careful about addressing some of the common stereotypes that kids hold.
First of all, you want to address the idea that all Native Americans are the same. Imagine if your school did "European heritage day" and dressed all the kids in leiderhosen, because that's how all Europeans dressed -- or kilts, or berets, or whatever, or wooden shoes. Or better yet, you put them all together and had people wearing berets, leiderhosen, kilts, and wooden shoes all at the same time. If you want kids to learn about Native American traditions, you probably want to be clear which traditions they're learning about -- perhaps pick one group from each region, or focus on traditions from your region.
Second you want to address the idea that Native American culture is either static or dead. Often times we portray images of Native Americans from the old days, but don't take the time to specify that Native Americans still exist and live in modern ways. My son's school did a nice project to address this -- last year the 3rd and 4th graders put on tableaus to show some of the ways the cultures have changed, and some things that have been constant. So, for example, they had children in costume show Iroquois people from the old days harvested and prepared the "Three Sisters" -- corn, squash, and beans, and then they showed a modern Iroquois family, in modern clothing, preparing the same food using modern appliances.
Another issue you want to be careful about is the issue of what is "sacred" in Native American tradition. When we were growing up, for example, a common assignment was to have kids write their own Native American story -- something that's akin to having a child write their own bible story (imagine if kids came home from school saying "I made up a new story about Jesus, I think they should add it to the bible" -- for once both Christian and Atheist parents would have something they could oppose together). Similarly, in many Native American cultures, ceremonial garb is considered sacred, so dressing a child up can be quite offensive.
OK, this probably wasn't much help at all. If you can answer the questions above, I might be able to provide some more thoughts.
When people try and portray what native Americans were like during the first Thanksgiving then they are portraying them correctly by wearing the clothing they wore "back then." I don't see how that can be offensive to anyone in this day and time. In order to portray it correctly you would try and wear clothing as close to same time in history as you can. I don't see that as offensive.
