Religion is no different from other ethical systems in this regard. Most parents want to pass their values onto their children and, where those values are broadly acceptable to society, society expects parents to do this, and criticises those who do not. Hence we try to teach our children not to resort to violence, to be respectful of others, etc. But we go slightly further; we do not simply teach them to behave in this way, but to believe that it is right and good to behave in this way. This is, broadly, true whether parents are religious or not.
Is this “indoctrination”? If you like to call it that, it is. But virtually all parents do it, and are expected to do it. If the parents’ ethical system is religiously based, then they will seek to pass that on; likewise if their ethical system is founded on (say) secular humanism, that is what they will offer the child.
What will differ, I think, is how tolerant parents will be of children who, when they reach the age of reason, question or reject the system which their parents offer them. Some will be understanding, supportive or even encouraging of this; others will be angry, upset or challenged by it. To some extent, but only to some extent, this depends on the particular belief system which the parents have. If they have a narrow, rigid system which holds that only acceptance of very specific beliefs and values is right and good, and the children reject those values, they will be upset (because they think their children will suffer as a result) and they will be ashamed (because they will feel that they have failed their children). It also depends on the parents own personalities and characters.
Even where parents are angered by their childrens rejection of the values offered to them, I doubt that they would argue that the children owed an obligation to the parents to accept the belief system in question, as the OP asks. I suspect that they would consider that the children owed an obligation to themselves, to certain immutable values or to a god-figure but (unless the belief system involves ancestor-veneration) not to the parents.
The stereotype of parents upset by their children’s ethical beliefs is of fundamentalist religious parents upset by their children adopting different religious beliefs, or becoming indifferent to religion. Like most stereotypes, there is a good measure of truth in it. However the reverse also occurs; some parents who consider themselves liberal find themselves intolerant of fundamentalist religious views adopted by their children.
Basically, we want our children to be like us, only better. I believe this is a univeral wish. It is a difficult but important lesson to learn that our children can be unlike us, and still better.