Yahshua (Jesus) was from the "Nazarene Essene Village", south and at the base of Mt Carmel. There were 3 Religious sects in Israel. Pharisees. Sadducees and Essenes. There were 2 Essenes settlements. One in the North as mentioned and the other near the River Jordan in south. John the Baptist was said to not recognize Yahshua. They were both of the Essene's Sect. John recognized Yahshua's mannerisms and dress but since he was not of Johns sect he did not recognize him. Essenes did not believe in eating flesh (meat) or in animal sacrifices.
Answer
I had heard the theory that John had been raised by the Essenes near the Dead Sea, and may have held some of their beliefs. I had never heard this about Jesus, although it appears to be commonly thought that there was some Essene influence on his teachings. Just because he was raised in Nazareth doesn't mean it was necessarily in the Essene community, since Nazareth itself was larger and had many people who were not Essenes. It would seem that he was not of the Essenes for several reasons. His teachings were more in line with those of the Pharisees than of the Essenes. He certainly did not oppose animal sacrifice, because he told a leper to offer the sacrifices commanded when he had healed him (Luke 5:14). He ate animal flesh (Luke 24:42-43, as well as references to eating the Pesach/Passover.) He and his disciples did not follow the Essene views of washings or of strict observance of Sabbath (Luke 6).
If John was an Essene, then Jesus was most likely not. “And the Lord said, Whereunto then shall I liken the men of this generation? and to what are they like? They are like unto children sitting in the marketplace, and calling one to another, and saying, We have piped unto you, and ye have not danced; we have mourned to you, and ye have not wept. For John the Baptist came neither eating bread nor drinking wine; and ye say, He hath a devil. The Son of man is come eating and drinking; and ye say, Behold a gluttonous man, and a winebibber, a friend of publicans and sinners!” (Luke 7:31-34) He was so different from the Essenes that he was even accused of overindulgence in alcohol.