Depends on what is meant by "required". That may seem pedantic, but there is a world of difference between the historic Christian view on the one hand: that Holy Baptism is a precious Sacrament which Christ instituted through which God acts and works to bring us from death to life by placing us in Christ, working faith in our hearts, and giving us the foundation of our walk with God by faith by the Spirit; and the view of certain sectarian groups which present Baptism as a work, another notch we must mark in order to earn salvation from God. Every mainstream, historic Church confesses the necessity of Baptism and that Baptism is salvific--a rejection of this view exists only among certain Protestant traditions of the past few centuries who view Baptism either as a covenantal sign or as a symbolic act of obedience. So when I say it depends on what is meant by "required" is this: The historic Christian confession is that Baptism is required because Christ specifically commands His Church to make disciples, baptizing them; and Scripture attaches God's promises to this Sacrament and these promises convey salvific reality: forgiveness of sins (Acts 2:38), being buried, dead, and raised with Christ (Romans 6:1-3), being clothed with Christ (Galatians 3:27), and that it saves (1 Peter 3:21); not on account of it being a work of righteousness we do in order to win something from God (an ordinance) but on account of it being God's own gracious action toward us (a Sacrament). Baptism is not required in the sense that if a person happens to not receive Baptism then they cannot be saved, otherwise we would be speaking damnation for all the many martyrs who died before receiving Baptism, and that would be wickedness to speak in such a way of such beloved saints of God. So a church that treats baptism as a human work required in order to flip on a magic "saved" switch teach falsely; but the historic faith of God's Church has always been the biblical teaching that Baptism is a precious Sacramental means of grace through which God brings us into Christ and, in Christ, His Church.
Unfortunately these two diametrically opposite views are often confused together in certain polemical teachings.
As a Lutheran I believe, quite strongly, that Baptism is necessary. Scripture tells us plainly what Baptism is and what Baptism does, and receiving this gift of Baptism is not an act of symbolic obedience but is a profound act and work of God by His Spirit, whereby God's word is brought together with ordinary water and God does something for us. Namely: All the promises we can find in the plain text of Holy Scripture. This does not, however, mean all unbaptized persons are un-saved; because that's simply untrue. God works through His Means of Word and Sacrament, that means hearing the word is also a Means of Grace--a divine action by which God's word comes to us, united in the ordinary preaching of a minister of the Gospel. It's not the words of a man that saves us, it's the word of God (Romans 10:17); it's not water that saves us, it's the word of God (Ephesians 5:26, 1 Peter 3:21), etc. And yet God has chosen that His word be united to mundane things: preaching, water, bread and wine. So to pretend as though the water doesn't matter when God says it does; or to pretend the preaching of the word doesn't matter when God says it does, etc is in violation with God has given and revealed. So while water does not save, when God unites His word with water, and we have this precious sacred thing--Baptism--then we can trust in what God has promised here in His gift, in this sacred thing God does and gives. So when we read that we are born again "by water and the Spirit" in John 3:5 we can trust the Lord who tells us this: it's not either water or Spirit, it's water and the Spirit because the Holy Spirit is Himself living and active and at work here.
Consider the many times, throughout the Bible, where God uses ordinary things to accomplish His extraordinary purposes. Jesus took dirt and spit and placed it on the eyes of a blind man and the man was healed of His blindness. Does dirt and spit heal blindness? Of course not--and yet here ordinary dirt, mere spit, are brought together with Christ's word to heal blindness and the man gained his sight. God works through the completely ordinary. He always has.
He didn't ordain angels to be His witnesses to all nations, He ordained a group of uneducated fishermen, a lowly tax-collector, rebels, and nobodies. He didn't even choose special people, He chose ordinary people. God has always used the ordinary to accomplish His extraordinary works. Recall even with the ancient Prophets, like Elijah--it was not in the earthquake, the thunder, or the howling winds that God was found--but in the still tiny whisper. God used Moses, a man who himself said he was bad at speaking in order to proclaim His wonders to Egypt. God didn't call a king from Ur, but a pastoralist named Abram and Sarai his barren wife. God always takes the lowly and makes it lofty.
