Is it ever okay to tell an unfaithful Christian, "You are going to Hell if you do not repent of your sins†and come back to the church?"
People have a tendency to want to make rules to simplify decisions, but sometimes rules can't cover every situation.
Generally, we aim for gentle, polite persuasion to convince someone to leave sin. "But avoid foolish and ignorant disputes, knowing that they generate strife. And a servant of the Lord must not quarrel but be gentle to all, able to teach, patient, in humility correcting those who are in opposition, if God perhaps will grant them repentance, so that they may know the truth, and that they may come to their senses and escape the snare of the devil, having been taken captive by him to do his will" (II Timothy 2:23-26). But there are times when a person is so caught up in sin or so stubborn, that they refuse to see the danger in front of them. There are times when stronger measures are needed.
Consider the example of John: "But when he saw many of the Pharisees and Sadducees coming to his baptism, he said to them, "Brood of vipers! Who warned you to flee from the wrath to come? Therefore bear fruits worthy of repentance"" (Matthew 3:7-8). This has all the elements that you mentioned, and John wasn't wrong for tell the Pharisees about their sins and their consequences. Jesus also spoke strongly at times, "Woe to you, scribes and Pharisees, hypocrites! Because you build the tombs of the prophets and adorn the monuments of the righteous, and say, 'If we had lived in the days of our fathers, we would not have been partakers with them in the blood of the prophets.' Therefore you are witnesses against yourselves that you are sons of those who murdered the prophets. Fill up, then, the measure of your fathers' guilt. Serpents, brood of vipers! How can you escape the condemnation of hell?" (Matthew 23:29-33). Then consider Paul: "But Elymas the sorcerer (for so his name is translated) withstood them, seeking to turn the proconsul away from the faith. Then Saul, who also is called Paul, filled with the Holy Spirit, looked intently at him and said, "O full of all deceit and all fraud, you son of the devil, you enemy of all righteousness, will you not cease perverting the straight ways of the Lord?" (Acts 13:8-10). Therefore, harsh criticism is sometimes needed.
Yet, there is something wrong with saying that individual is going to Hell. That puts the speaker in the Judgment Seat that belongs only to Christ. None of us can condemn someone to eternal punishment. We can rightly say that God states that a person who commits certain deeds and remains unrepentant will end up in Hell, but there we are only relaying what God already said. "Of how much worse punishment, do you suppose, will he be thought worthy who has trampled the Son of God underfoot, counted the blood of the covenant by which he was sanctified a common thing, and insulted the Spirit of grace? For we know Him who said, "Vengeance is Mine, I will repay," says the Lord. And again, "The LORD will judge His people." It is a fearful thing to fall into the hands of the living God" (Hebrews 10:29-31). But to personally condemn anyone is wrong because we don't have the right to make such a statement. Consider the example of Michael: "Yet Michael the archangel, in contending with the devil, when he disputed about the body of Moses, dared not bring against him a reviling accusation, but said, "The Lord rebuke you!"" (Jude 9). Michael would not put himself in God's Judgment Seat, even concerning Satan, whom the Lord has already condemned. If an archangel knew better than to do this, then we too must not over extend ourselves.