Yes. It is wrong.
To greet is to offer someone a polite word of hailing. It’s an expression of goodwill. I think greeting goes beyond mere goodwill. I would define a greeting as an endorsement of a situation or someone’s existence and the continuation of the situation or his/her existence albeit in a better way.
When you wish someone ‘Happy birthday’, you are rather saying ‘I’m glad you exist and I wish you live long in a healthier and wealthier way than now.’ Ditto with wedding anniversary wishes.
But, can a Christian truly greet people of other faiths on their festival days without compromising on his inherent Scriptural beliefs and faith? The Bible teaches us that the way to heaven is only through Jesus Christ, the Son of God. Acts 4:12 says: “Nor is there salvation in any other, for there is no other name under heaven given among men by which we must be saved.”
Jesus Himself says in John 14:6, “I am the way, the truth, and the life. No one comes to the Father except through me.” He is not a way, as in one of many ways around us; He is the way, as in the one and only. No one, regardless of reputation, achievement, special knowledge, or personal holiness, can come to God the Father except through Jesus.
Jesus spoke of Himself as the only way to heaven in several places besides John 14:6. He presented Himself as the object of faith in Matthew 7:21–27. He said His words are life (John 6:63). He promised that those who believe in Him will have eternal life (John 3:14–15). He is the gate of the sheep (John 10:7); the bread of life (John 6:35); and the resurrection (John 11:25). No one else can rightly claim those titles (From GotQuestions).
A Christian’s rightful boast that his religion is the true religion comes from Jehovah God’s affirmation that He is the Lord and there is no other (Isaiah 45:5).
Isaiah 43:10, 11 say: ‘Before Me there was no God formed, nor shall there be after Me. I, even I, am the Lord, and besides Me there is no savior.’
While some Christians greet their friends of other faiths on their festivals quite ignorantly without realizing what they are doing, a few others quote 1 Corinthians 9:19-23 as the basis for their action. They say, ‘If I don’t identify myself as their friend, how can I win them over to Christianity?’
In 1 Corinthians 9:19-23 Paul says: ‘For though I am free from all men, I have made myself a servant to all, that I might win the more; and to the Jews I became as a Jew, that I might win Jews; to those who are under the law, as under the law, that I might win those who are under the law; to those who are without law, as without law (not being without law toward God, but under law toward Christ), that I might win those who are without law; to the weak I became as weak, that I might win the weak. I have become all things to all men, that I might by all means save some. Now this I do for the gospel’s sake, that I may be partaker of it with you.’
Becoming all things to all men is a great way to win souls for Christ. But it should not be at the cost of your soul! Misapplying this passage has led many to stray away from their faith. It is the equivalent of frequenting a bar to preach Christ to a bunch of alcoholics. What’s the guarantee that the evangelist won’t fall to the charms of the glistening drink? Do not look at wine when it is red, when it sparkles in the cup and goes down smoothly (Read Proverbs 23: 31-35). Or rather the equivalent of visiting brothels and gallivanting with call girls ostensibly to bring them to Christ. Nothing would be more offensive to your own soul than these disastrous ‘mission’ outreaches. It is good to remember that we are, after all, mere mortals and fallible human beings.
What Paul meant in the passage above is to empathize with those to whom you are preaching Christ, not joining forces with them. The Bible definitely does not teach us to live like a sinner to win a sinner.
That being the case, a Christian wishing someone of another faith on his festival would be the equivalent of saying, ‘I’m glad you believe in the myth surrounding the festival. And, I wish you continue to live a life of spiritual ignorance and bondage.’
If we truly wish and pray that they shall know the Truth (Jesus) and the Truth shall set them free, we will not want to wish them on their festivals surrounding imaginary beings and mythical happenings.
Romans 14:23 says: ‘…for whatever is not from faith is sin.