Is Krishna a Hindu?
As you'll find in more detail here, the word "Hindu" isn't found in Vedic literature. When we speak of Krishna, we're referring to the Supreme Person, the Absolute Truth, the ultimate source of all energies.
"Hindu" is a relative term referring to customs and beliefs of a portion of the population of Southeast Asia. It came into use in relatively recent history. The Supreme Person, God, isn't bound by time or space, so He can't be referred to as "Hindu," "Christian," or "Muslim."
Some believe the Absolute Truth to be ultimately impersonal, and that Krishna is merely a historical personality appearing in India to teach "Hinduism." In answer to this, Krishna Himself says in the Bhagavad-gita,
"Unintelligent men, who do not know Me perfectly, think that I, the Supreme Personality of Godhead, Krishna, was impersonal before and have now assumed this personality. Due to their small knowledge, they do not know My higher nature, which is imperishable and supreme."
"They say Krishna is Indian or Krishna is worshiped by the Hindus and therefore He is one of the Hindu Gods; and they think that Krishna is saying, "Yes, I am the Hindu God. Yes, I am Indian." But He is like the sun. Why American sun or Indian? Nothing is American or Indian; that is all artificial."
—Krishna Consciousness, the Topmost Yoga System, 4
"Krishna is not sectarian. Krishna is not Hindu; Krishna is not Indian; Krishna is not African. Krishna is nothing of this material world. He is the Supreme Personality of Godhead, transcendental. Simply by knowing Krishna, one becomes immediately liberated and goes back to Krishna. . ."
— Srila Prabhupada, from a lecture given on Bhagavad-gita, 7.3 in Bombay on February 18, 1974