"Pursue . . . the holiness without which no one will see the Lord." Hebrews 12:14
"Nothing unclean . . . shall ever enter into [Heaven] . . ." Revelation 21:27
Dispensationalism and Charismatic churches teach the lie about "carnal Christians," as if there are two classes of Christians. There are not! You are either a Christian or you are not. You are either holy, or you are carnal and worldly. It is impossible to be both. Those who teach the lie of a "carnal Christian" should try reading their Bible closely some time and paying attention to what it actually says, because it contradicts their doctrines of demons.
Romans 8:13 says, "for if you are living according to the flesh, you will die; but if by the Spirit you are putting to death the deeds of the body, you will live." The flesh and the Spirit are constantly contrasted and opposed to one another. Being of the flesh is always negative, while being in the Spirit is always positive. As long as you are living in and according to the flesh, your destiny is eternity in Hell. If you submit to the Holy Spirit and conform your life to that of Christ, practicing holiness and putting sin to death, your destiny will be eternity in Heaven.
A "carnal Christian" is living according to the flesh. Ergo, these people will die and spend eternity in Hell. A "carnal Christian" is not pursuing holiness, let alone the holiness required in order to see the Lord. Ergo, they will never see the Lord. A "carnal Christian," living according to the flesh and lacking holiness, is unclean. Ergo, they will never enter Heaven.
Ergo, they were never "Christian" to begin with
Without holiness, no one will see the Lord. Nothing impure or unclean will ever enter into Heaven. "Test yourselves to see if you are in the faith; examine yourselves! Or do you not recognize this about yourselves, that Jesus Christ is in you—unless indeed you fail the test?" (2 Cor. 13:5). If you are genuinely a Christian, you will pursue/strive for that holiness that will enable you to see the Lord. The Greek word means to suffer persecution "for that holiness without which no one will see the Lord"; to press forward "for that holiness without which no one will see the Lord."
Bank on this fact: there is no such thing as a "carnal Christian." It's an oxymoron; a contradiction in terms. This is an excuse used for the sinful behaviour of false converts who have been Pope-ishly declared to be "Christian" when no transformation has ever taken place in their lives.