What are the various beliefs about the fate of honest atheists?

My church is in the Free Methodist denomination, which (out of the categories you list) would best be characterized as "Evangelical." The short blunt answer is that such a person would be condemned:

Whoever believes in him [Jesus] 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. This is the verdict: Light has come into the world, but people loved darkness instead of light because their deeds were evil. Everyone who does evil hates the light, and will not come into the light for fear that their deeds will be exposed. But whoever lives by the truth comes into the light, so that it may be seen plainly that what they have done has been done in the sight of God.

(John 3:18-21)

On the human level we tend to value honesty and sincerity as innately virtuous things, so it's easy to look on an "honest atheist" and feel some level of respect -- and then to feel it unfair that God would condemn such a person. But that's the human level of thinking. We forget two things:

1. Honesty and sincerity are morally neutral, not innately virtuous. A person for example can be honestly and sincerely selfish, proclaiming without shame "I'm in this for me, myself & I." Or a person can be honestly and sincerely racist... or honestly and sincerely a bully... etc.

2. People are endlessly deceptive not only toward each other, but even to themselves, about their motives. "I was just trying to be nice and stop her from tripping," said the teenage boy who grabbed hold of a pretty girl at school -- and maybe he even believes it himself. The same applies to the hypothetical "honest atheist." Deep down, why does this person disbelieve? Is it because he's examined the evidence with a careful eye? Has he examined any evidence at all? Or does he simply reject the idea of a God who could validly claim 'ownership' over himself and try to run his life for him? Does he have private vices that he simply refuses to give up no matter what?

According to Christian perspectives you mentioned, a person who claims that Jesus Christ was not in any way divine, and that his death was not spiritually meaningful in any way cannot enter into the Body of Christ, Community of Saints, or the Kingdom of God.

Consider the following soteriological perspectives,

Salvation by faith: regardless of other principles or teaching, most self proclaimed adherents to mainstream Christian religions require that a person acknowledges that they believe in the resurrection of Christ and some of its consequences.

Repentance from Sin: While most Christian groups acknowledge that salvation is by faith alone (Reformed, Evangelical, Catholic), some acknowledge that a person should have a life after conversion in which their behavior is altogether different than that of their pre-conversion life.

Decisionalism: Yet other Christian groups, and some of those also mentioned, teach that a person must make a conscious decision to follow Jesus, and that each should be able to point to a moment of realization of the truth and salvation.

Lordship: Others yet claim that Salvation comes when people turn their lives over to Christ, as their Lord and Master.

Sanctification: If a person obtains justification from sin by their sanctification, a person must become holy by living a biblically driven life, their sins being forgiven because of their dedication to godliness.

If an atheist does not fall into any of these categories, most of the Christian groups that operate according to any one of these doctrines, including the Reformed, Evangelical, Catholic, or Orthodox churches, as well as others like Mormonism, would not include such a person among those who, according to many of these groups, will continue to live eternally in communion with God.

I would study how each denomination interprets this passage of John 10:

24 So the Jews gathered around him and said to him, “How long will you keep us in suspense? If you are the Christ, tell us plainly.” 25 Jesus answered them, “I told you, and you do not believe. The works that I do in my Father's name bear witness about me, 26 but you do not believe because you are not among my sheep. 27 My sheep hear my voice, and I know them, and they follow me. 28 I give them eternal life, and they will never perish, and no one will snatch them out of my hand. 29 My Father, who has given them to me,[a] is greater than all, and no one is able to snatch them out of the Father's hand. 30 I and the Father are one.”

The disagreements are over how a person becomes one of God's sheep (election or free will). The agreement is that the sheep recognize their shepherd's voice. Failure to recognize the voice of Jesus is the defining mark of a person who is not one of Jesus' sheep. To a sheep, it is a self-authenticating recognition of the identity of the savior. If you hear his voice and recognize it, then to say you do not recognize it is to lie and be dishonest. If you do not recognize the voice, then you are not one of the sheep, but instead one of the goats. The goats in Jesus' other parable are decidedly not honest.

You have asked about the fate of a soul that has "honest disbelief". I don't know what it means for disbelief to be "honest". I doubt you will find the above traditions addressing such a concept. However, you also describe the person in question as an "explicit denier of Christian truth". According to Scripture, such people do not have eternal life:

Luke 10:15-17: And you, Capernaum, will you be exalted to heaven? You shall be brought down to Hades. The one who hears you hears me, and the one who rejects you rejects me, and the one who rejects me rejects him who sent me.

John 12:48-50: The one who rejects me and does not receive my words has a judge; the word that I have spoken will judge him on the last day. For I have not spoken on my own authority, but the Father who sent me has himself given me a commandment — what to say and what to speak. And I know that his commandment is eternal life. What I say, therefore, I say as the Father has told me.

1 John 2:22-25: Who is the liar but he who denies that Jesus is the Christ? This is the antichrist, he who denies the Father and the Son. No one who denies the Son has the Father. Whoever confesses the Son has the Father also. Let what you heard from the beginning abide in you. If what you heard from the beginning abides in you, then you too will abide in the Son and in the Father. And this is the promise that he made to us — eternal life.

Perhaps in speaking of "honest disbelief", what you are trying to get at is the fact that some people, presented with Christian truth, simply find themselves unable to believe and trust Jesus to save them. We cannot force ourselves to believe what we do not believe, and no one can trust Jesus to save them without first believing they need saving and that he is able to save them. Then, perhaps you are thinking that, this being so, how can God hold unbelievers accountable? Paul responds to essentially that question in Romans 9, especially verse 19 and following. The answer is not that they are not held accountable for their unbelief. If that were so, Paul's answer to the question, "Why does he still find fault?" would be quite different.

If you are such a person and you a feeling a desire to believe yet feel unable to believe, it may be God is working on you. To such a person, I would say, call on God for mercy and pray for faith - ask, seek, knock and it will be opened to you (Luke 11:9-13).

As far as I am aware, both Evangelical and Reformed Christians believe what the Bible says in John 3:18:

Whoever believes in him [Jesus] is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God. (ESV)

Basically, there are only two groups - those who have been saved by coming to faith in Christ Jesus, and the unsaved.

The Evangelical and Reformed churches I have attended do not promote the idea of universal salvation. Salvation is all about faith. There is only one sin that cannot be forgiven, and that is the sin of unbelief.

The Evangelical Alliance (U.K.) makes these unambiguous declarations:

The justification of sinners solely by the grace of God through faith in Christ.

The personal and visible return of Jesus Christ to fulfil the purposes of God, who will raise all people to judgement, bring eternal life to the redeemed and eternal condemnation to the lost, and establish a new heaven and new earth.

Source: https://www.eauk.org/about-us/basis-of-faith