Ask any religionist if he has been indoctrinated, and he will swear that he hasn't. The word 'indoctrination' is something that religionists recoil from. It's something bad, and it's certainly not what they do to their children. To them, indoctrination means something like brainwashing. Like what the Soviets did to their citizens to turn them into loyal comrades, or what many Arabic nations do in their public schools to make them hate Jews. But definitely not what happens in Sunday School.
There are a number of ways to define 'indoctrination'. In the most general sense, it simply means inculcation. To impress values, ideas, or methodology in someone, often by rote or repetition. This does not necessarily carry any negative connotation, and it's not pejorative. It is something we have all experienced in some form, and it's nothing to be defensive about. So instead of just denying it, religionists should at least ask: "What do you mean by 'indoctrination'?"
There certainly can be a more negative sense of the word that involves unquestioning or uncritical acceptance of beliefs, and resistance to any alternative ideas. If taken to an extreme, it could be called brainwashing. This is the kind of indoctrination that religionists get defensive about, and adamantly deny that they do it to their children, or that they have ever been subjected to it themselves. They regard the term as pejorative, and they insist that it's not appropriate use that word with regard to religious education. As one of them puts it:
Is it OK to raise your offspring in such a way that their adult views will (hopefully) mirror your own? For millennia, this was called "civilizing the next generation". Now it's accused of being brainwashing or indoctrination. - MortalWhy should they be so defensive about this if it doesn't apply to their benign religious education? Sure, there has been some criticism of religious indoctrination by people like Richard Dawkins. But I don't hear anybody calling for a ban on raising children with religious beliefs or instilling parents' values into their children. Perhaps it would be worthwhile for religionists to ask themselves what the criticism is really about. It isn't about all benign religious teaching. It isn't about simply passing your values and beliefs on to your children. But it is undeniably true that there can be detrimental effects from religious teaching, in addition to the beneficial ones.
One such effect that Dawkins talks about is uncritical acceptance of beliefs before the child has the intellectual ability to decide whether those beliefs are reasonable. They become so deeply embedded that it is nearly impossible to rationally evaluate them in adulthood. Dawkins argues that this can be intellectually limiting to the child. Even many hard-core religionists would agree that some religious beliefs (such as YEC or biblical literalism) can be intellectually unsound. But are they willing to admit that someone who has been indoctrinated with those beliefs has been damaged or limited in some way?
Of course, the religionists always deny that they have been indoctrinated, or that their own critical faculties have been limited by their religious beliefs. In fact, most of them will insist that they have critically examined their own beliefs, and arrived at the conclusion that those beliefs are fully rationally justified. So while they may not take the Old Testament stories literally, they have no problem accepting the literal truth of the fantastic tales in the New Testament. Most will tell you that in fact it is atheists who are unable to question what they believe because they don't accept the truth of those stories.
Religionists are deluded. They could no more critically examine their religious beliefs than they could stop breathing. Why? Because they have been thoroughly indoctrinated. (And note that I am not referring to all people who have been raised with religious beliefs. Some can be quite reasonable.) But there is no clear distinction between benign religious education and the kind of teaching that crosses the line into the territory of brainwashing, even if those who do it don't think that's what they're doing. Some people are more heavily influenced by their indoctrination than others. Hard-core religionists are essentially brainwashed. They are fully invested in their childhood beliefs, and resistant to any evidence or argument that would cast those beliefs into doubt. They will never abandon those beliefs under any circumstances, no matter how overwhelming the evidence is, or how reasonable the argument. That's real indoctrination.