In two communities in Canada that I've experienced, the songs and dances exhibited at public powwows are not the authentic sacred dances that have been passed down through generations as part of spiritual practice. They're exhibitions, created dances that are not intimately connected to the group's sacred beliefs. The songs and drumming that accompany them are also different from the authentic sacred songs. So public participation is okay, it's just that most outsiders don't think that they're not really participating in an authentic ceremony.
They celebrate similar things like community and respect for nature, so the public gets a glimpse at what the group values through dance. But they're created for show and profit, and the true sacred dances are fiercely guarded and never publicly displayed or even filmed when performed in private.
Exhibition dances are often much more flamboyant and colourful than the true dances because that's what attracts outside interest. The sacred dances, I've been told, are more subdued but are danced with far more reverence. Certain families also have a duty to learn and pass on sacred dance while exhibition powwow dance is more like a hobby that's not necessary.