Do I believe Atheists are going to hell?

[SteveII]

According the the NT, you go to hell because of the condition you are in (the separation that sin has caused from God's perfect holiness). The only way to bridge that separation is to do something about the cause of the separation. The only thing that can erase the effect of sin is the redemption offered by Jesus' sacrifice. This takes an act of the will to accept it. There is no room at all in this concept for an "honest effort...but not convinced". Believing that there must be makes us feel better, but has literally zero support in the NT.

I agree with the "condition you are in", but as I tried to explain earlier, I don't think this hinges necessarily on belief vs disbelief, when the disbelief is an honest mistake. Don't you think a person can be in a state of grace if they strive to do good? If they love others, if they love truth? Isn't accepting love and goodness a form of accepting God without realizing it?

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For the record, this is what Catholic Answers has to say. And they are super conservative/err on the side of caution about everything:

https://www.catholic.com/qa/can-an-atheist-go-to-heaven

You edited your post while I was typing...here was my response to the original:

No I don't think that striving to do good or making an honest effort is enough. "State of Grace" is the state where you are made holy before God because of a very specific act: accepting Jesus as your savior and the redemption that comes with it (that's the Grace part). A position such as the one you suggest actually unravels the whole core of Christianity and all the various doctrines become internally inconsistent. 

I don't disagree at all with the statement in the link you posted.  "Invincible ignorance" is the description of people who did not have an opportunity to hear (such as remote peoples or babies and young children). This does not apply to most adults on earth. Most have heard the gospel and many have rejected it. 

Some verses that illustrate my points:

Romans 6:23 NKJV – For the wages of sin [is] death, but the gift of God [is] eternal life in Christ Jesus our Lord.

For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life. For God did not send his Son into the world to be its judge, but to be its savior. (John 3:16-17)

Romans 10:9 If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. 10 For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved.

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Full Question

My question is this: can an atheist go to heaven? Thank you for your time.

Answer

If someone does not come to believe in God because of stubbornness or refusal to give up selfish desires, then such a person would be culpable for his lack of belief.

If, however, because of circumstances a sincere person is prevented from coming to belief in God, then his lack of faith is called invincible ignorance, and such a person would not be considered culpable.

As Pope Pius XI noted in Quanto conficiamur moerore:

"It is known to us and to you that those who are in invincible ignorance of our most holy religion, but who observe carefully the natural law, and the precepts graven by God upon the hearts of all men, and who being disposed to obey God lead an honest and upright life, may, aided by the light of divine grace, attain to eternal life; for God who sees clearly, searches and knows the heart, the disposition, the thoughts and intentions of each, in his supreme mercy and goodness by no means permits that anyone suffer eternal punishment, who has not of his own free will fallen into sin."

https://www.catholic.com/qa/can-an-atheist-go-to-heaven

Ok, I edited this about a million times.

A bit about Invincible Ignorance (I had to look it up because it is not a phrase protestants use--but the concept is the same in both branches of Christianity):

The term "invincible ignorance" has its roots in Catholic theology, where [...] it is used to refer to the state of persons (such as pagans and infants) who are ignorant of the Christian message because they have not yet had an opportunity to hear it. The first Pope to use the term officially seems to have been Pope Pius IX in the allocution Singulari Quadam (9 December 1854) and the encyclicals Singulari Quidem (17 March 1856) and Quanto Conficiamur Moerore (10 August 1863). The term, however, is far older than that. Aquinas, for instance, uses it in his Summa Theologica (written 1265–1274),[1] and discussion of the concept can be found as far back as Origen (3rd century). https://en.wikipedia.org/wiki/Invincible..._theology)

The key criteria in your original quote is "because of circumstances" and not "a sincere person".