For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
I know a young woman who does not claim to be an atheist though she might as well.
A Catholic who denounced her faith & has embraced the cult "Unity School of Christianity (USC)" because there was a similarity between her Catholic upbringing & the spirit-ism of USC.
USC was created by Charles Fillmore who said of GOD that He dwells in all things; of the Holy Spirit, that He is not a personal being, only an impersonal force; of Christ, He was merely a perfect man.
While she considers herself to be a Christian, her "faith" is in a "pseudo" relationship with a spirit force that is not personal & offers nothing. I shared the gospel with her as often as the opportunity presented itself.
She once invited me to "hug a tree" with her because she believes peace & power can be obtained from a tree. She speaks bitterly about most of her life, once saying that I always seem to have such peace & joy, in spite of the fact that my husband is in the latter stages of cancer. When I offered the reason (1 Peter 3:15), she got angry & ended our relationship.
Now that she has closed the door between us, I have had to "shake the dust" from my feet and go on. I pray each day that by His Spirit, someone will come to her and she will receive them with great joy.
The word atheist comes from the Greek, "atheos", which means "godless."
It is my belief that anyone involved with any "religion" other than Christianity is truly "godless", hence is an atheist!
If dealing with person who claims to be an atheist, or a freethinker, who also scoffs at the Holy Ghost and is proud of doing it, we may avoid further contact. That is what the apostle Paul said on several occasions that our prayers for them would be useless.
Lord Jesus told us that in His days, there are people having eyes and ears but can't see or hear or understand His miraculous teachings as it is already determined ages ago by the ancient prophets.
Not wanting to be contentious, I ask you for the verses where Paul said that prayer for scoffers & unbelievers was "useless."
On the contrary, I find that his admonition to pray for scoffers & unbelievers was obvious when you consider Romans 10:1.
No one was more guilty of scoffing & unbelief than Israel. Yet, Paul said, "Brethren, my heart's desire & prayer to GOD for Israel is that they may be saved."
If he thought prayer for folks such as those was useless, he wouldn't have wasted his time.
1 Thess. 5:16-18 tells us to "pray without ceasing" & in Luke 18, Jesus Himself, in the parable of the persistent widow & the "unjust" judge, said that "men always ought to pray & not lose heart."
When we pray we are turning toward GOD's face.
In 1 Cor. 4 Paul said the LORD is the judge & we are to judge nothing (vs.5) "before the time, until the LORD comes" to "reveal the counsels of the hearts."
Those who do not have a relationship through faith with GOD in Christ truly can't pray. They may speak words that sound like prayer, but GOD does not hear them. (John 9:31)
GOD does not need our wills to become known to Him, He already knows our heart for He knows all things (1 John 3:20). But what He does want is for His desires to become our own.
And it is His desire that "all men be saved & come to the knowledge of the Truth." (1 Tim. 2:4)
Paul did say to "withdraw" ourselves (1 Tim 6:4-6) from "useless wranglings of men"
He did not say prayer for them was useless!