Do I believe Atheists are going to hell?

[SteveII]

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. 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.

I don't see how invincible ignorance is simply just someone who has never heard of God/Jesus, especially the way it was framed on the link lol.

The link described a person culpable for lack of belief as someone who is being stubborn about it or not wanting to bother with the moral lifestyle that would come with it.

...Not as someone who has heard of Jesus but wasn't able to sincerely come to believe it's all real. That sounds more like the person being described as having invincible ignorance.

I guess on this we will just have to disagree. I personally don't see how a person who otherwise strives for truth and strives to live a moral life can be damned forever for an honest mistake. I think such person is accepting Christ in a way, by accepting love and goodness and truth.

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".