There are a few agitators in most tribes but in general if you treat their heritage with respect they are not offended. And it certainly is not "racist". Every native I have ever known in my life personally (and there are a lot) is a fan of the Cleveland Indians, or the Atlanta Braves or "gasp" the Washington Redskins. In fact when I played HS ball there was a reservation high school whose varsity team was the warriors and JV was the Braves. There was another team further north that called themselves the Indians.
Generally I think most of the Ute traditions are lame, like 3rd Down Jump, the MESS, raping blow up dolls and going topless at games. But I think a tribal day at one game per year would be a great Ute tradition.