This is another much-debated issue. Many say he was not saved, some say maybe, and others say yes. We are never told in Scripture that he was not a believer. I think there is evidence that he was because, though he sold his birthright, he did seem to believe in the Abrahamic covenant and its blessings which would suggest faith. The prime evidence for this is the scheme that took place between Isaac and Esau to give him the blessings of the covenant in spite of the previous prophecy that Esau, the firstborn, would serve the younger.
The problem with Esau was that he was dominated by his fleshly appetites. What he lost or forfeited was his inheritance, but he was still Issac’s son and one who evidently still believed in the reality of the Abrahamic covenant for he later sought his inheritance with tears though he never really changed his mind (repented) about the priority of spiritual things. As Eric Sauer put:
“Doubtless, birthright [inheritance right] is not identical with sonship. Esau remained Isaac’s son even after he had rejected his birthright. In fact, he received, in spite of his great failure, a kind of secondary blessing (Gen. 27:38-40b).” (Quoted in The Reign of the Servant Kings, by Joseph Dillow.)
Thus, the author of Hebrews uses him as an illustration to genuine Christians of the danger spiritual blessings and serving faithfully as Christians. This use suggests that he was saved. The author of Hebrews was not questioning their salvation. He was confident they were saved and once saved, always saved, but one’s inheritance in God’s kingdom may change considerably with the loss of rewards, etc.
12:15-17. As a grim reminder of what can happen among believers, the writer warned that one who misses the grace of God may become like a bitter root whose infidelity to God affects others. Here the author had in mind Deuteronomy 29:18 where an Old-Covenant apostate was called a “root . . . that produces such bitter poison.” Such a person would be godless (bebeµlos, “profane, unhallowed, desecrated”) like Esau, Jacob’s brother, whose loose and profane character led him to sell his inheritance rights as the oldest son for the temporary gratification of a single meal. He warned the readers not to yield to transitory pressures and forfeit their inheritances. If some did, they would ultimately regret the foolish step and might find their inheritance privileges irrevocably lost as were Esau’s. This would of course be true of one who ended his Christian experience in a state of apostasy, which the writer had continually warned against. (The Bible Knowledge Commentary.)