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The VigilantCitizen article about this film covers some interesting aspects of a Hindu protest of the use of the  Bhagavad Gita that was pulled from the film after a protest (big ups to Conspirazzi for enlightening me to this). VC also goes into some Crowley-sex magick stuff too:

The interior scenes of the party were shot at Elveden Hall, a private house in the UK designed to look like an Indian palace. When the “festivities” begin, a Tamil song called “Migration” plays in the background, adding to the South-Asian atmosphere (the original version of the song contained actual scriptural recitation of the Bhagavad Gita, but the chant was removed in the final version of the movie). This peculiar Indian atmosphere, combined with the lascivious scenes witnessed by Bill as he walks around the house, ultimately points towards the most important, yet most hidden part of the movie: Tantric Yoga and its Western occultism derivative, Sex Magick. This last concept was “imported” by British occultist Aleister Crowley and is now at the center of the teachings of various secret societies:

“Aleister Crowley’s connections with Indian Yoga and Tantra were both considerable and complex. Crowley had direct exposure to some forms of these practices and was familiar with the contemporary literature of the subjects, wrote extensively about them, and – what is perhaps the most important – he practiced them. In his assessment of the value of Tantra, he was ahead of his time, which habitually considered Tantra a degenerate form of Hinduism. Instead, he claimed that, “paradoxical as it may sound the Tantrics are in reality the most advanced of the Hindus”. Crowley’s influence in bringing Eastern, primarily Indian, esoteric traditions to the West extends also to his incorporation of the elements of Yoga and Tantra into the structure and program of two influential magical orders, the A.:A.: and the OTO.”
– Martin P. Starr, Aleister Crowley and Western Esotericism

The above quote stipulates that Tantric concepts were incorporated in two important secret societies: the A.:A.: and the OTO (Ordo Templi Orientis). The OTO is still extremely influential in elite circles and reaches the highest levels of politics, business and even the entertainment industry. At the core of these orders is the Thelema, a philosophy created by Aleister Crowley that he summed up with the saying “Do What Thou Wilt”.  This saying is actually a translation of “Fais ce que tu voudras” the motto of an 18th century secret society, the infamous Hellfire Club.

The Hindu protest was claiming that…

When thousands of Hindus watched the latest movie by Nicole Kidman and Tom Cruise, “Eyes Wide Shut” they were stunned.  While they have been admirers of the stars, what lay ahead, was completely unexpected.

The orgy scene in the middle of the movie has the recitation of the verse from the Bhagwad Gita, one of the most revered Hindu scripture.  The shloka

Parithranaya Saadhunam Vinashaya cha dushkrithaam Dharmasamsthabanarthaya Sambhavami yuge yuge

which means :

“Whenever there is a decline of Dharma and the rise of Adharma,O Arjun, then I Shree Krishna manifest (or incarnate) Myself. I incarnate from time to time for protecting the good, for transforming the wicked, and for establishing Dharma”