All the indoctrination and "political correctness" in the world will not change the fact that a child has a different relationship and need between the child's father and the child's mother. There is no one like a father in a child's life, and there is no one like a mother. This is true whether or not the child is the biological child or if there are complicated familial relationships. Every child needs his or her father and every child needs his or her mother.
To a child the mother is the image of love and security, because the mother is the giver of life to the child and the child is totally dependent on the mother both biologically and emotionally. The mother unlocks for the child the reality of being alive and of having both awareness and feelings that are safely expressed and understood.
To a child the father is the image of love and strength, because every child looks up to his or her father, regardless if the father is the strongest guy on the block, or the biggest bread winner or not. Babies are able to perceive love from each parent, and indeed they need love from each parent. But babies are also able to perceive the gender based difference between the mother and the father and indeed to do so is a survival trait that is the gift of millions of years of evolution. Humans look to the father for love that comes in the form of protection and instruction. Humans look to the mother for love that comes in the form of emotional security. It is stupid and self defeating to argue otherwise.
Both parents have roles therefore in the faith formation of their child. Children must be introduced to the reality of God at the earliest age and instructed in their family faith by both parents. There is a valuable nuance of difference in roles between the father and the mother in teaching of faith, however, one that used to be natural and instinctive, but one which now requires awareness to be made and reinforcement.
As the father figure who provides both love and strength, protection and physical security to the child, father has a particularly valuable perspective to give to his young child about God. The father should teach the child how "even daddy has someone that he looks up to for strength and protection, and that is God." Thus the child learns that there is someone so strong and reliable that even his father looks up to him and turns to him for protection. So that is the nuance that gives great dimension and perspective to the child that is unique to the father figure. Traditionally that is taught in Christian families in the context of explaining God and St. Joseph to the young child. God helps St. Joseph to protect the young baby Jesus. Children can instantly understand that, as they feel that their protection comes from their fathers.
Throughout the faith history of the Abrahamic religions (Judaism, Christianity and Islam) it is the father's responsibility to ensure that the child is raised from its first days to know about God, to love and respect God, and to know the tenets of their faith. Notice I say it is the responsibility of the father; this does not mean that he is the one who does everything and has this duty as some sort of privilege of gender. Of course not and in fact, it is the mother who often provides the most quantity of religious instruction to the child. But what I am explaining is that "the buck stops here" in the well organized, loving and God fearing family, for it is the father who is ultimately responsible for how well or how poorly the child is instructed in God and his or her faith. This is why it is important for the father to explain the context and reality of God to the child at the earliest age that the child can understand, and in child appropriate ways and language of course. The father ensures that the child understands that daddy believes in God, that daddy has a relationship with God and looks to God for protection and strength, and that daddy makes sure that the child receives all that he or she needs to learn and practice their faith.
The mother has the equally important role, recognizing that nuance is complimentary rather than competitive with the father. For example, the mother is often the one to explain to the child the questions the child will later ask about human relationships from the mother, such as "Where does God come from," "Does God have a mommy and daddy," and "What is heaven like?" We all know that children tend to ask personal and intimate questions from the mother. Thus by working together the father and the mother give a fully dimensional and complimentary faith formation to the child. Another typical place that children tend to learn their faith is that mom is often the one to help them with their prayers before bed. Traditionally, moms would help with the night prayers while dads helped with saying grace before meals. That was how it was in my home, where my stepfather always ensured that grace was said at dinner, while mother's role was the night time routine with the before bed prayers.
I know that many are thinking, "Oh how Ozzie and Harriet. That's not how it is today." Well, yes and no. I am presenting the ideal, but it is the living and real ideal that worked for two thousand years and more. This is not a cool idea of mine; it is an explanation to you of how things actually worked in the Jewish, Muslim and Christian faiths for many hundreds of years. The father always had the responsibility to leverage the role modeling that he provided by virtue of simply being a father and from that perspective teach the child how father has a relationship with God that he can count on, and ensuring that the child had access to religious instruction and worship service.
Also, remember that lifespans were much shorter and unpredictable in the hardships of more primitive times. It's only in the last century that the norm was to have both parents have a good chance of avoiding early deaths from illness, conflict, poverty and in the woman's case, childbirth. So there were many households that did lose a mother or a father and yet this pattern was followed. How was that done? Obviously in the time of responsible extended families the loss of a father meant that uncles or grandparents took over the religious instruction and responsibility. There was no "gap" in the father's role to ensure religious instruction and the basics of belief in God from the earliest age. Likewise if the mother died due to illness or childbirth, or from wearing out in hardship as many men did of the time too, aunts and grandmothers equally ensured that the child had the portion of religious formation that came from the mother, with the maternal nuance that is to be expected. Older brothers and sisters also had a great responsibility and role in raising their younger siblings in the faith. And this was not a chore but a welcome activity even among children, since they enjoyed their piety and religious instruction within the family. (Remember that for most of human civilization there was no "entertainment" media, like adventure books. Children enjoyed Bible stories as children today enjoy "adventure" stories. So children loved the Bible and reading about saints because they were nonfiction adventure, to put it in a modern analogy of terminology). If you read the lives of the saints you will see that many had influential siblings and how they shared their joy in God.
There is another point I want to make about the Catholic Church's emphasis on the Communion of Saints, especially the veneration of St. Joseph and his spouse, the Blessed Virgin Mary. During the times where there were frequent deaths of a parent due to the primitive and harsh conditions of life prior to this past modern century, the child would often turn to Joseph or Mary to be their heavenly parent if one of their earthly parents perished. Thus a Catholic child who lost their father would often look toward St. Joseph as their substitute for their real father, and the child who lost their mother would look toward Mary as their substitute for their real mother. Thus there was a great comfort and role modeling provided by the Communion of Saints that complimented the roles of the earthly extended family. You can read examples of this again in the lives of the saints and other literary sources. Popes who lost one of their parents, especially the mother, have mentioned that they felt as a child or a young man a turning toward Mary as their "mother" in lieu of their own mother's earthly presence.
This is another reason why it is so vital to a child's well being to introduce them to God and instruct them in God and their faith at a very early age. Previous generations gave their children a stability of faith formation that is essential to not only spiritual well being of the child, but also their physical, mental and emotional well being. The saints were real people and real role models and, as Catholics do, teaching the child that they are "part of the family" and part of the extended family in spirit as well as the physical extended family gives the child a bulwark against feelings of extreme isolation, existentialism and alienation when life gets rough. You don't have to be a social scientist to see that the past several generations have been robbed of that right and that reality. That's why the sacrament of Baptism is performed for infants in the Catholic Church. It is not the water and the oil itself, but it is the heralding of the beginning of the child's religious instruction and privileges of knowing the Communion of Saints as their own family too. Catholics adhere to the Jewish tradition and faith that the parents instruct the children in their faith and initiate them through ritual into the faith from their very birth. (Prior to baptising the equivalent was the presentation of infants in the temple and the sacrifices made on their behalf). There is no foundation in any of the three Abrahamic faiths for "waiting" until the child "decides on their own" to have a "personal relationship with God." That very idea would have been a total scandal among Jews, Christians and Muslims.
I hope that this has given you something to think about. Fathers need to remember that there is real dignity in fatherhood and much of it comes from the God given duty that they are ultimately responsible for their child's faith formation. God frowns on the idea that boys or men think that their pride comes in being a "baby daddy" and that's it. Regardless of the circumstances of the conception, if you are old enough to be a "baby daddy" you are old enough and therefore responsible for raising the child within faith in God (and that applies whether "you" "fully believe or not.") Analogy: you give your infant milk to drink even though you may not drink milk yourself. I mean, duh.
Likewise this is not to shortchange mothers or their role and dignity in the faith formation of their children. I'm putting the onus on both parents to understand that everyone has to do more, and do more earlier and consistently for their children. It is a scandal how, even in my own family, children were raised without their faith or even being baptized. Societal "revolution" and breakdown have cheated children of their birthright in knowing God and practicing their faith. Not raising your child in your institutional mainstream faith is dumber, not smarter, low scale, not "sophisticated," depressive and not "enlightened," oppressive and not "liberating." To raise children so that they don't know of God and his love, guidance and security is scandalous and is one of the worst forms of "parental malpractice." It's also self defeating because it robs you as a parent of one of the greatest joys that parents have, and have attested to throughout the centuries, which is introducing your infants to God and teaching your children his ways, how to make their way in the world, and how to hope for achieving the Kingdom of Heaven in their turn when their time comes.
I hope that you found this helpful. It's never too late, by the way, even with grown children. Tell them what you both have missed out on and learn about God together, wherever you are and in whatever stages of life's journey.