You misunderstand the New Testament.
Have a look at the following verses just from John as an example.
Please notice the word, "believe", in each verse.
John 1:7
He came as a witness to testify concerning that light, so that through him all might believe.
John 1:12
Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God—
John 1:50
Jesus said, “You believe because I told you I saw you under the fig tree. You will see greater things than that.”
John 2:11
What Jesus did here in Cana of Galilee was the first of the signs through which he revealed his glory; and his disciples believed in him.
John 2:22
After he was raised from the dead, his disciples recalled what he had said. Then they believed the scripture and the words that Jesus had spoken.
John 2:23
Now while he was in Jerusalem at the Passover Festival, many people saw the signs he was performing and believed in his name.
John 3:12
I have spoken to you of earthly things and you do not believe; how then will you believe if I speak of heavenly things?
John 3:15
that everyone who believes may have eternal life in him.
John 3:16
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.
John 3:18
Whoever believes in him is not condemned, but whoever does not believe stands condemned already because they have not believed in the name of God’s one and only Son.
John 3:36
Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God’s wrath remains on them.
John 4:21
“Woman,” Jesus replied, “believe me, a time is coming when you will worship the Father neither on this mountain nor in Jerusalem.
John 4:39
Many Samaritans Believe
Many of the Samaritans from that town believed in him because of the woman’s testimony, “He told me everything I ever did.”
John 4:41
And because of his words many more became believers.
John 4:42
They said to the woman, “We no longer believe just because of what you said; now we have heard for ourselves, and we know that this man really is the Savior of the world.”
John 4:48
“Unless you people see signs and wonders,” Jesus told him, “you will never believe.”
John 4:53
Then the father realized that this was the exact time at which Jesus had said to him, “Your son will live.” So he and his whole household believed.
John 5:24
“Very truly I tell you, whoever hears my word and believes him who sent me has eternal life and will not be judged but has crossed over from death to life.
John 5:38
nor does his word dwell in you, for you do not believe the one he sent.
John 5:44
How can you believe since you accept glory from one another but do not seek the glory that comes from the only God?
John 5:46
If you believed Moses, you would believe me, for he wrote about me.
John 5:47
But since you do not believe what he wrote, how are you going to believe what I say?”
John 6:29
Jesus answered, “The work of God is this: to believe in the one he has sent.”
John 6:30
So they asked him, “What sign then will you give that we may see it and believe you? What will you do?
John 6:35
Then Jesus declared, “I am the bread of life. Whoever comes to me will never go hungry, and whoever believes in me will never be thirsty.
John 6:36
But as I told you, you have seen me and still you do not believe.
John 6:40
For my Father’s will is that everyone who looks to the Son and believes in him shall have eternal life, and I will raise them up at the last day.”
John 6:47
Very truly I tell you, the one who believes has eternal life.
John 6:64
Yet there are some of you who do not believe.” For Jesus had known from the beginning which of them did not believe and who would betray him.
John 6:69
We have come to believe and to know that you are the Holy One of God.”
John 7:5
For even his own brothers did not believe in him.
John 7:31
Still, many in the crowd believed in him. They said, “When the Messiah comes, will he perform more signs than this man?”
John 7:38
Whoever believes in me, as Scripture has said, rivers of living water will flow from within them.”
John 7:39
By this he meant the Spirit, whom those who believed in him were later to receive. Up to that time the Spirit had not been given, since Jesus had not yet been glorified.
John 7:48
“Have any of the rulers or of the Pharisees believed in him?
John 8:24
I told you that you would die in your sins; if you do not believe that I am he, you will indeed die in your sins.”
John 8:30
Even as he spoke, many believed in him.
John 8:31
Dispute Over Whose Children Jesus’ Opponents are To the Jews who had believed him, Jesus said,
“If you hold to my teaching, you are really my disciples.
John 8:45
Yet because I tell the truth, you do not believe me!
John 8:46
Can any of you prove me guilty of sin? If I am telling the truth, why don’t you believe me?
John 9:18
They still did not believe that he had been blind and had received his sight until they sent for the man’s parents.
John 9:35
Spiritual Blindness
Jesus heard that they had thrown him out, and when he found him, he said, “Do you believe in the Son of Man?”
John 9:36
“Who is he, sir?” the man asked. “Tell me so that I may believe in him.”
John 9:38
Then the man said, “Lord, I believe,” and he worshiped him.
John 10:25
Jesus answered, “I did tell you, but you do not believe. The works I do in my Father’s name testify
If you read John 20:31 you will see that John wrote specifically about faith, trying to persuade people to believe in Jesus as the Christ. None of those scriptures in John CANCEL OUT what is written in Revelation, nor any other part of the Bible. They do not make the scriptures in Revelation untrue. Do not pit one part of the Bible against another as if they compete with each other. ALL of God’s word is true. Just because John says we must believe that Jesus is the Son of God, does not mean that we do not have to obey Him! How did you come to THAT false conclusion??
John also tells us that JESUS says, “ If you love me, KEEP MY COMMANDMENTS.” John 14:15. And again, “You are my friends if you DO WHAT I SAY!!” John 15:14. So, even John understands that obedience is necessary to salvation. Who is going to be saved if you don’t love God or if you are not a “friend of God”? And Jesus plainly makes that conditional upon “OBEDIENCE.”
John has just proved that he believes obedience is necessary to salvation. So unless he is contradicting himself, the scriptures you gave do NOT disprove the necessity of obedience.