In societies such as the U.S. where religion, especially theism, is an important cultural component, the roots of this belief system are planted in most people at a very early age such that just past toddler-hood, many (most?) children are already taught by their families to recite simple prayers to a god who they are also told will punish them if they misbehave and / or fail to adhere to certain rituals.
Theists have long understood the importance of indoctrinating young minds. Francis Xavier, the founder of the Roman Catholic Jesuits order, is credited with the motto "Give me a boy until he is seven and I will give you the man". Among Orthodox Jews, boys customarily began Torah study at age four. My grandfather was one of them, and no doubt his zealous piety was likely the result of this intense education. That happened well over a century ago; yet such thought control practices continue into the modern era. It may sound like an overreaction on my part that I feel sad when I see little kids already dressed in religiously traditional garb before they can even understand what's going on. But IMO such apparel is symbolic of the oppression to which their young minds are just starting to be conditioned.
These are just a few examples of hereditary religion, and some atheists assert that such training is brainwashing and a form of child abuse. However, devout parents may respond that freedom of religion entitles them to raise their children as they see fit, and as such they have the right and the duty to instill a godly morality in them. Further, they may argue that the state has no right to dictate to them how to practice such parental obligations (short of prohibiting demonstrable cruelty). And in fact, doesn't this argument cuts both ways? Can't it be used by atheist families to protect their rights to bring up their kids as non-believers? For them this freedom is an important bulwark especially in the "red" states Christian where privilege prevails and church-state separation is frequently violated.
That is why the case for legal challenges to hereditary religion is difficult to make. So rather than fruitlessly trying to compel parents from indoctrinating their children, as distasteful to nonbelievers as such practices might be, atheists need to try to counter that kind of setting when children are outside the home. One way to do this is by advocating the requirement that public schools proved a strictly secular education.to their students with special vigilance against creationism being taught in the classroom. Another step is promoting the revocation of tax exempt tuition for religious schools. Normally, such expenses are not tax deductible, but may be under certain circumstances. (IMO donations to religious institutions should be tax-exempt under no circumstances). This won't prevent parents and these institutions from inculcating religious belief in their children, but it will send a message that doing so comes at a price (literally and figuratively) and that secularists will no longer accept the burden of paying the shifted taxes for which these families should be responsible.
As long as there are religious believers, they will likely try to pass their faith on to the next generation, and in itself that's not necessarily a guarantee that their kids will not eventually kick over the trances and become atheists. Many nonbelievers were onetime theists, myself included. Realistically, we can't interfere with the family life of believers without being accused of proselytizing. So all that secularists can do is work to provide a public environment where kids are encouraged to think and question the myths that they've been taught to accept as the truth. If doing so can help even a few of them overcome their theistic upbringing, it will be well worth the effort.