The definition of Christian is someone that believes in Christ,
This is YOUR definition not Christs' definition. And since we are discussing what constitutes a Christian, his words are what matter not yours or muslims or mine.
Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.22Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works? 23And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
Belief that Jesus existed and even doing good works in his name doesn't make a person a Christian, or make them covered by the new covenant.
Jesus answered and said to him, “Most assuredly, I say to you, unless one is born again, he cannot see the kingdom of God.”
4 Nicodemus said to Him, “How can a man be born when he is old? Can he enter a second time into his mother’s womb and be born?”
5 Jesus answered, “Most assuredly, I say to you, unless one is born of water and the Spirit, he cannot enter the kingdom of God. 6 That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. 7 Do not marvel that I said to you, ‘You must be born again.’ 8 The wind blows where it wishes, and you hear the sound of it, but cannot tell where it comes from and where it goes. So is everyone who is born of the Spirit.” .... “He who believes in Him is not condemned; but he who does not believe is condemned already, because he has not believed in the name of the only begotten Son of God. 19 And this is the condemnation, that the light has come into the world, and men loved darkness rather than light, because their deeds were evil. - Jesus
A person who does not give up all that he has, he cannot be Jesus disciple. And, this is what it takes to be born again. A Christian divests himself from his rights and is able to say without hypocrisy, "do with me what thou wilt".... fully submitted for better of for worse.
Who says acceptance of the covenant is fundamental? Scriptures such as Acts 16:31, John 17:3 shows it is belief in Jesus.
And the beliefs we choose to accept PROVE whether or not we believe Jesus. If Jesus says to enter into an agreement with him "for the forgiveness of sins" his sheep will listen to him and do it. They will not listen to another voice indefinitely, even if there was some initial confusion.
Further, JWs do accept the New Covenant, they just believe it is mediated to them through the anointed.
Again, Jesus says something else:
For there is one God, and one mediator between God and men, the man Christ Jesus;
The agreement that Jesus mediates between God and Men is the identifying factor of what makes it possible for a anyone to survive judgment. Those that are destined for this pardon, are called Christians.