Yes it is intolerant. In fact, it is very intolerant to say that Jesus is the way the truth and the life and that no one can get to God except through Him as Jesus Himself said in John 14:6. It is also intolerant to state that there is no other name under heaven other than Jesus by which a person can be forgiven of his sins as Peter said in Acts 4:12. It is intolerant to say that there is only one true God as Jesus said in John 17:3.
It is also intolerant to say that trying to enter into heaven by any other way than Jesus is to be a thief and a robber as Jesus said in John 10:1. Jesus was intolerant when He said that He is the one who reveals God to people (Luke 10:22). Jesus was even more intolerant of religious hypocrisy when He condemned the religious know-it-alls and called them hypocrites and deceivers (Matt. 23:25-26). Jesus was extremely intolerant of the buying and selling in the temple when He drove the people out of it by force and overturned their money tables (John 2:13-16). Jesus was intolerant of hatred when He said: "love your enemies" (Luke 6:27). Jesus was intolerant of ignorance when He taught the people truth (Matt. 5). Jesus was intolerant of prejudice when He gave the parable of the Good Samaritan (Luke 10:30-37).
Yes, Christianity is intolerant because its founder, Jesus, was intolerant. Christianity is intolerant of false gods and false gospels. Why is it so intolerant? Because it is shaped after Jesus. It is intolerant because there is a hell and Jesus, who is God in flesh (John 1:1,14; Col. 2:9), who died for our sins (1 Pet. 2:24), has made the only way to forgiveness a reality: through Him alone (John 14:6) and without Him comes damnation.
On the other hand, Christianity is very tolerant. It teaches to be very forgiving (Matt. 18:21-22), to be patient and kind (Gal. 5:22-23), and to be honest and wholesome (Phil. 4:6-8). Jesus taught us to love and to heal and to be examples of kindness and truth in the world. Jesus was intolerant of religious hypocrisy and bigotry. He was very intolerant of false teachers. He was intolerant of pride, rebellion, sin, covetousness, adultery, lying, cheating, stealing, fornicating, and murder. He was intolerant of husbands treating their wives poorly. He was intolerant of pain and was saddened by suffering. Yet, at the same time, He demonstrated the greatest love and patience with those who were guilty of all these things. Why? Because He is God in flesh, incarnate love, incarnate righteousness, incarnate humility.
The whole issue of whether or not Christianity is intolerant lies in who Jesus is, what He claimed, and what He did. If what Jesus said and did is true, then Christianity isn't intolerant. It is simply true and it is the world that is intolerant of that truth.
Likewise, it is true that Jesus lived. It is true that Jesus walked on water (Matt. 14:25-27). It is true that Jesus healed the sick (Matt. 8:5-13). It is true that Jesus calmed a storm with a command (Mark 4:39). It is true that Jesus raised the dead (Matt. 9:25; John 11:43-44). It is true that Jesus claimed to be God (John 5:18; 8:24; 8:58 -- see Exodus 3:14). It is true that Jesus was killed on a cross (Luke 24:20). It is true that Jesus rose from the dead (Luke 24:39; John 20:27). These are not feeble claims made by crazy people who wanted to gain power and fame. These are the claims of Christ Himself and of those who followed Him and suffered for Him and died for Him.
Either it is all true or it is not. Either Jesus performed miracles or He did not. Either Jesus rose from the dead or He did not. Based solely and completely on who Jesus is and what He did, Christianity is the truth and by necessity all other religions that disagree with Jesus are wrong.
Truth is, by nature, intolerant of falsehood. If Christianity is not true, then Jesus was not God, then Jesus did not do miracles, then Jesus did not heal the sick, then Jesus did not walk on water, then Jesus did not die and rise from the dead after three days. But, if He did do these things, then Christianity alone is true since in all the religions in the world, only Christianity has the person of Jesus and Jesus said that He alone was the way, the truth, and the life (John 14:6).
Christianity is only as intolerant as Jesus is true.