My thoughts here aren't polemic so much as just entering the discussion. While we come to different conclusions in some regards, I salute your willingness to question what you were taught. It takes a strong will, as well as willingness to change, to do so.
The challenges in developing good discernment can be daunting, if one is willing to question what they think they know. And all of us have been indoctrinated. To deny it is delusional.
Part of the challenge is to not throw away the baby with the bathwater. There are aspects you speak of here that are not bad or nefarious. They just exist. Memorization, for instance, is a good tool. Songs are as well. It's more about content and purpose. But even these can be twisted by wrong ideologies.
We also tend to swing like a pendulum. If we see something wrong in one area of our thoughts, we can tend to gravitate to the opposite. However, the truth often lies in a more balanced perspective. There are absolutes, but our challenge at assessing them accurately is swayed by our experiences, preunderstanding, presuppositions, programming, etc.
I stand among a small minority who are Christian libertarians. There are a few of us here on Steemit, which has been somewhat refreshing. On one hand, we're told by those who share our faith that our perspective is incompatible. IMO, they fail to see their own statism as the idolatry that it is.
On the other hand, our fellow libertarians also see it as incompatible, for obvious reasons (many of which you touched on). I won't get into the theology, because I don't think this is the place. But I am open to a respectful dialogue on it, if desired.
The thing is, if the teaching is true, is it indoctrination? For instance, we learn the ABCs through repetition and song. They are not objective truth, but it's certainly helpful. We learn to count through repetition.
We also learn proverbs, metaphors, idioms, etc. through repetition and sometimes song. These are applicable to life, sometimes holding objective truth while at other times subjective "norms".
So where is the balance? IMO, it's based on the verity of what we're taught. As we mature, it's our responsibility to investigate it all and discern for ourselves what is true and what is a lie. Interesting, you and I both did that at similar stages in our lives. I embraced Christ but eventually rejected the state. You rejected both.
Not sure that adds much value to the discussion. Your ideas and proposals just made me think, so I figured I'd jot down those thoughts as well.
As for the last question:

If you discover you were probably indoctrinated, do you think it’s ethically responsible to actively change your views?

Yes... No...
As noted earlier, we're all indoctrinated. But the burden is discerning the truth and adjusting accordingly, whether our views change or not. More than likely, some will be solidified while others are rejected. The challenge is finding the truth in the midst of the overwhelming array of opinion, hypotheses, theories, propaganda, indoctrination (truth as well as lies) and emotional strain that we can face as a result.