You are correct in your quotation, but I think belief in Christ must show a commitment to Christ and that can be shown by the works we do which can be just having conversations face to face or as we do on this forum.Romans 10:
9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
10 For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.
Baptism is important and while I would not say that without baptism Jesus is not going to reject everyone, I would say, that if you recognize baptism is something Jesus did and said that it was necessary to do in order to fulfill all righteousness why not do it? Better safe than sorry.
Jesus final instruction to his disciples was: (Mark 16:15) And he said unto them, Go ye into all the world, and preach the gospel to every creature. (16) He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
This is why I think a true and full belief is; submitting to baptism, just as Naaman had to dip himself seven times in the river Jordan before he was healed of leprosy.
Baptism is a simple act of faith which is done before witnesses and is an outward sign of an inward belief. "At the end of the day" and "in the final analysis" as they say; it is what is in a person's heart that will count in the day of judgment. I think it is wise to obey than disobey. I think we should obey the requests of Jesus of which two are; 1)to be baptized and 2) to remember him by taking bread and wine.
Jesus says; "this do in remembrance of me" and whilst that instruction was given to his immediate disciples, we see it was carried out by the Apostle Paul.
1 Corinthians 11:
23 For I have received of the Lord that which also I delivered unto you, That the Lord Jesus the same night in which he was betrayed took bread:
24 And when he had given thanks, he brake it, and said, Take, eat: this is my body, which is broken for you: this do in remembrance of me.
25 After the same manner also he took the cup, when he had supped, saying, This cup is the new testament in my blood: this do ye, as oft as ye drink it, in remembrance of me.