Here were my own thoughts on seeing the above:
where’s the section called “the racism”?
My first reaction was “Oh look, only white passing Indi… WAIT, THOSE ARE WHITE PEOPLE REPRESENTING MY CULTURE!”. White people representing my culture, I am not surprised, I’m merely mildly infuriated.
First, I respect the reaction, and believe me this bothers me a fair bit as well.
But we can do more than simply label it "racism." Are we unhappy because these are white dancers performing Indian characters, or because of the whole context of this ballet -- including its original choreographer (the Russian Marius Patipa), as well as the modern choreographers and designers who have produced the Paris Opera Ballet's 2012 version (from which these Gifs are derived)?
This is a ballet called La Bayadere, first performed in 1877. It's part of a long tradition in European high art of using "exotic" Indian themes and settings with all white casts. (Another classic example is the opera Lakme.) It was produced as a reaction to a visit from real temple dancers to Russia in the 1870s.
Such stories are usually based on actual Indian sources. While there are many elements of La Bayadere that are clearly historically inaccurate (a Rajah's daughter would never be involved in dancing publicly, as the character does in this ballet), it's not entirely out of the question that a story like this could be recuperated and rethought to make it more relevant and 'true' to real Indian culture.
A future version, for example, might rework some of the original choreography using elements from classical Indian dance formats. And yes, use dancers of Indian origin. (Presumably one reason why they might not be casting any Indian dancers is that there may not be very many who are trained at this level in western ballet. If they change some of the choreography to include Indian classical dance, the complexion of the cast could look very different.)
In short, I'm not thrilled about what I'm seeing in the images above, but maybe this Gif series might be an opportunity to get educated, not just mad.