YES. It was 100% intentional. I highly recommend reading up on the making of this film. There was an incredible amount of care that went into the development.
They had Lakota consultants for the project, especially regarding the use of the Lakota language in the film (which is used sparsely, but when used is accurate).
It’s par for the course now to consult people belonging to a culture for projects representing it these days (i.e. Moana, Frozen 2, etc.) but it certainly wasn’t when Spirit came out in 2002.
This film is allegorical to its core.