I don't think the poster was referring to "classically liberal" which would be closer to libertarian.
"We hold these truths to be self-evident, that all men are endowed by a creator with certain unalienable rights."
The Founding Fathers thought that government must serve the people because people are created in God's image.
It will be impossible for you to extricated Christians from rationality, science, philosophy, and education in the West as they dominate all of it from the fall of the Roman Empire to the 19th century.
Further, why called indoctrination?
His seems like a rhetorical (pronounced "propagandistic") strategy common to the New Atheist.
The point is to get the opponent (the Christian parent) to accept such a poisoned term! And no more work need to be done to convince the weak-minded whether they be on the fence atheist or dies in the wool.
Do we live on an external world? Prove it.
Do we believe in other minds (that other people exist besides ourselves)? Prove it.
Do we believe in the reality of the past? prove it.
These and the very presuppositions that logic is based on are not provable. And unless we adjust our epistemic justification level (what we count as provable) we are going to have nothing to teach our children whatsoever!
So to your question why do we need to teach if it is true?
You seem to think religious knowledge is obtained through some sort of osmosis.
Much mathematical knowledge is true so why do we teach math? Science, history, literature.
Obviously because we are beings that are able to scaffold knowledge over time to more accurately describe the external world around us. It can take decades to get from basic addition to a quantum mechanical description of the small-scale forces of our universe.
There are a dozen theories or so floating about the QM world. Suppose I teach the Copenhagen model, to my high school senior who is taking an AP Physics coarse. Am I indoctrinating him or her?
Of coarse not. As a parent, regardless of religious ideology, one tries to advance the child's way in the world by given them the most true beliefs and fewest false ones.
With theism and particularlyJudeo-Christian religions, God's existence, best explains:
1 - the evidence for the beginning of he universe from nothing 13.7 billion years ago,
2 - the fine-tuning of the initial constants and laws to support life
3 - the existence of objective (culturally independent) morals,
4 - the nature of my soul or consciousness being immaterial
5 - the universal desire for meaning and purpose humans have.
There are many other inferences to the best explanation of the external world we see that are experienced by Christians such as miracles and certain types of evil, and profound experiences of God.
As to your point of seeing Christian complain that others aren't raising their children properly, (those pesky Christian butinskis) did you miss the fact that your whole post is you telling all Christians "how to raise their kids." Was this meant to be a test to see if we could spot hypocrisy?
As to apologetics and the work of the HS one wonders given your track record above how sincere you are. But the apologetics is considered useful when people have certain rational limitations that are trapping them into a false internal construction of the world. So helping people eliminate false beliefs, such as the false belief that there is no God, is as simple a question to answers as the question I alluded to earlier, "why teach math?"
If someone let's say Larry Krauss, says "the universe came from nothing, and I can prove it, nothing is a vacuum, there was a high-energy state, in a false vacuum (see I used the word vacuum) can produces Higgs particles fluctuating into and out of existence, therefore the universe created itself."
(a universe forNothing)
Apologetics can point out that Krauss' "Nothing," includes space, time, QM laws, a false vacuum, and high-energy states that are unstable.
Nothing means -having no (zero) attributes.
Using apologetics we can apply rationality to claims that the evidence point to need for something like God (Eternal, all-powerful, all-knowledgable, and personal (due to agency) is actually self-starting. Without apologetics, we would be unable to expose this argument as fallacious.
So we are just defending the inference that God best explains the external world we have.
Similarly the HS function qua non-Christians is to reveal knowledge that they are morally defective in a significant way (guilty of not meeting God's sand are, namely perfection MT 5:48) and that Jesus' death on the cross is God's only answer to our moral dilemma. That is it. The HS does these functions in largely unknown ways. Again, no osmosis knowledge here.
But your osmosis view is not without intuition. God does reveal something's about himself for everyone to perceive sans apologetics, indoctrination, or even H.S.
1. Certain universal moral values and duties. (Death camps are wrong)
2. The beauty and awe of nature points to God's existence and creativity.
3. Circumstances that create instant overwhelming fear of death ( fox holes being shelled by the enemy)
Birth of children are also often in this category. So you are right to bring up osmosis as a category, you have just extended that notion too far, that's all.
Hope this response helps and is on track in the info you were looking to receive.