Were there any schools of Shaiva, Shakti, or Tantric philosophy that advocated human sacrifice?
If so, what were their arguments?
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This excerpt from the Madhaviya Shankara Digvijaya, the traditional biography of Adi Shankaracharya, describes how Adi Shankaracharya went to Karnataka and encountered the Kapalikas, a Shaivite sect which practiced human sacrifice:
After a time, [Adi Shankaracharya] started towards the Karnataka country, but was warned by the king of Vidarbha that those regions were very dangerous, as they were full of Kapalikas who were followers of the cult of human sacrifice who condemned the Vedic religiod were, on the whole, a curse to humanity. They were not likely to tolerate the spread of the Acharya's influence in those regions.... He was soon opposed by Krachaka, the leader of the Kapalika cult. Krachaka was smeared all Vera with the ashes from the cremation ground, and in his hand were the skull and trident, the emblems of his cult.... [Krachaka said] "Without the offering consisting of the red lotus of a bleeding skull and liquor, how can the Bhairava, embraced by Uma, be pleased?" Thereupon king Sudhanva, who was accompanying the Acharya with his men, drove away Krachaka with the contemptuous words: "You wretch! Get away." ... Krachaka declared, flourishing his battle-axe, "I am not the famous Krachaka unless I reap a harvest of the heads of your fellows!"
But the Kapalika sect, like many Shaivite and Shakta sects, doesn't exists anymore, and its texts are lost, so we can't really examine its arguments.
On a side note, contrary to what some people claim, the Vedas do not prescribe human sacrifice; see my answer here.