Here’s an article by Paul Copan which points out how father presence/absence and father quality affects belief and disbelief in God.

Excerpt:

Seventh, the attempt to psychologize believers applies more readily to the hardened atheist.It is interesting that while atheists and skeptics often psychoanalyze the religious believer, they regularly fail to psychoanalyze their ownrejection of God. Why are believers subject to such scrutiny and not atheists? Remember another feature of Freud’s psychoanalysis — namely, an underlying resentment that desires to kill the father figure.

Why presume atheism is the rational, psychologically sound, and default position while theism is somehow psychologically deficient? New York University psychology professor Paul Vitz turns the tables on such thinking. He essentially says, “Let’s look into the lives of leading atheists and skeptics in the past. What do they have in common?” The result is interesting: virtually all of these leading figures lacked a positive fatherly role model — or had no father at all.¹¹

Let’s look at some of them.

• Voltaire(1694–1778): This biting critic of religion, though not an atheist, strongly rejected his father and rejected his birth name of François-Marie Arouet.
• David Hume(1711–76): The father of this Scottish skeptic died when Hume was only 2 years old. Hume’s biographers mention no relatives or family friends who could have served as father figures.
• Baron d’Holbach(1723–89): This French atheist became an orphan at age 13 and lived with his uncle.
• Ludwig Feuerbach (1804–72): At age 13, his father left his family and took up living with another woman in a different town.
• Karl Marx(1818–83): Marx’s father, a Jew, converted to being a Lutheran under pressure — not out of any religious conviction. Marx, therefore, did not respect his father.
• Friedrich Nietzsche(1844–1900): He was 4 when he lost his father.
• Sigmund Freud(1856–1939): His father, Jacob, was a great disappointment to him; his father was passive and weak. Freud also mentioned that his father was a sexual pervert and that his children suffered for it.
• Bertrand Russell(1872–1970): His father died when he was 4.
• Albert Camus(1913–60): His father died when he was 1 year old, and in his autobiographical novel The First Man, his father is the central figure preoccupation of his work.
• Jean-Paul Sartre(1905–80): The famous existentialist’s father died before he was born.¹²
• Madeleine Murray-O’Hair (1919–95): She hated her father and even tried to kill him with a butcher knife.
• We could throw in a few more prominent contemporary atheists not mentioned by Vitz with similar childhood challenges:
• Daniel Dennett (1942–): His father died when he was 5 years of age and had little influence on Dennett.¹³
• Christopher Hitchens (1949–): His father (“the Commander”) was a good man, according to Hitchens, but he and Hitchens “didn’t hold much converse.” Once having “a respectful distance,” their relationship took on a “definite coolness” with an “occasional thaw.” Hitchens adds: “I am rather barren of paternal recollections.”¹⁴
• Richard Dawkins (1941–): Though encouraged by his parents to study science, he mentions being molested as a child — no insignificant event, though Dawkins dismisses it as merely embarrassing.¹⁵

Moreover, Vitz’s study notes how many prominent theists in the past — such as Blaise Pascal, G.K. Chesterton, Karl Barth, and Dietrich Bonhoeffer — have had in common a loving, caring father in their lives.¹⁶

Not only is there that anecdotal evidence, but there is also statistical evidence.

Excerpt:

In 1994 the Swiss carried out an extra survey that the researchers for our masters in Europe (I write from England) were happy to record. The question was asked to determine whether a person’s religion carried through to the next generation, and if so, why, or if not, why not. The result is dynamite. There is one critical factor. It is overwhelming, and it is this: It is the religious practice of the father of the family that, above all, determines the future attendance at or absence from church of the children.

If both father and mother attend regularly, 33 percent of their children will end up as regular churchgoers, and 41 percent will end up attending irregularly. Only a quarter of their children will end up not practicing at all. If the father is irregular and mother regular, only 3 percent of the children will subsequently become regulars themselves, while a further 59 percent will become irregulars. Thirty-eight percent will be lost.

If the father is non-practicing and mother regular, only 2 percent of children will become regular worshippers, and 37 percent will attend irregularly. Over 60 percent of their children will be lost completely to the church.

Let us look at the figures the other way round. What happens if the father is regular but the mother irregular or non-practicing? Extraordinarily, the percentage of children becoming regular goesupfrom 33 percent to 38 percent with the irregular mother and to 44 percent with the non-practicing, as if loyalty to father’s commitment grows in proportion to mother’s laxity, indifference, or hostility.

[…]In short, if a father does not go to church, no matter how faithful his wife’s devotions, only one child in 50 will become a regular worshipper. If a father does go regularly, regardless of the practice of the mother, between two-thirds and three-quarters of their children will become churchgoers (regular and irregular). If a father goes but irregularly to church, regardless of his wife’s devotion, between a half and two-thirds of their offspring will find themselves coming to church regularly or occasionally.

A non-practicing mother with a regular father will see a minimum of two-thirds of her children ending up at church. In contrast, a non-practicing father with a regular mother will see two-thirds of his children never darken the church door. If his wife is similarly negligent that figure rises to 80 percent!

The results are shocking, but they should not be surprising. They are about as politically incorrect as it is possible to be; but they simply confirm what psychologists, criminologists, educationalists, and traditional Christians know. You cannot buck the biology of the created order. Father’s influence, from the determination of a child’s sex by the implantation of his seed to the funerary rites surrounding his passing, is out of all proportion to his allotted, and severely diminished role, in Western liberal society.

Basically, anyone who doesn’t have a benevolent, involved father is going to have an more difficult time believing that moral boundaries set by an authority are for the benefit of the person who is being bounded. The best way to make moral boundaries stick is to see that they apply to the person making the boundaries as well – and that these moral boundaries are rational, evidentially-grounded and not arbitrary. It is therefore very important to children to be shepherded by a man who studied moral issues (including evidence from outside the Bible) in order to know how to be persuasive to others. If you want your child to be religious and moral, you have to pick a man who is religious and moral. And it can’t just be a faith commitment that he makes, he can just lie about that. Women ought to check whether men are bound to what they believe by checking what they’ve read. A man usually acts consistently with what he believes, and beliefs only get formed when a man informs himself through things like reading.

My advice to Christian women is this. When you are picking a man, be sure and choose one who is already invested in Christian things and producing results. It’s very unlikely that he’s going to start from nothing after you marry him. If you value your kids, make a man’s interest in developing and acting on a Christian worldview the main thing you are looking for.