"The unbeliever simply needs to come into a personal relationship with Jesus Christ."
This may be the answer to the question: "How does one become saved?"
Now, granted, I think I perceive what the person means in answering the question this way. They mean to say the person needs to develop a "positive" relationship with Jesus Christ.
Grant me the next few paragraphs to at least appeal to you that this language is sloppy and perhaps not uniformly true.
We all HAVE a personal relationship with Jesus Christ. We are born enemies. While not a favorable relationship or one to which we would boast on our spiritual resume, it is true. Our relationship to Jesus is one of enemy, adversary, and rebel.
We all also HAVE a personal relationship with the Devil. We are his children. While not a favorable relationship or one to which we would boast on our spiritual resume, it is true.
You do not become a Christian be developing a personal relationship with Jesus. You already have one and it is not favorable to your eternal security.
You become a Christian by God's grace reaching you through the preached Gospel of His atoning sacrifice in the Person and work of Jesus Christ, His Son. In Him, by Him, and through Him only do we have peace with God and eternal life secured.
In response to this, yes, we respond by pursuing God for the first time as His Spirit cheers us on. We pursue Him because He first pursued us. We love Him because He first loved us. It is a relationship and it is personal. But it does not save.
Grace working through faith in Jesus alone saves.