If an opinion is being slowly but inexorably pushed on you from all sides by your captor over a long period of time, as part of an explicitly designed program of of propagandizing, it's brainwashing, regardless of the opinion's merit!
Besides, just as you hold your "must be provable" views dear, similarly the religious parent holds his or her religious views dear.
Adults just slow down the writting but we always try to fit in the social group that we are living. And that includes political opinions, faith, etc...
It is one of those "one person's X is another person's Y" comparisons: indoctrination/brain-washing, religion/cult, freedom-fighter/terrorist, cute cat / insane evil sharp edged ball of allergens, ...
A more passive form of indoctrination would be repeated explanation (with or without query/prompt) so explanation can become indoctrination depending on context, but I'll stand by my choice of words above.
"Where do rainbows come from" can be answered with the explanation "As a way to show God's promise to Noah never to flood the Earth again" or with the explanation "because sunlight refracts through water into all the different colors we can see" or with the explanation "invisible unicorns fly through the sky sometimes and leave rainbows where they've gone".
Many people would call one or more of these indoctrinations, despite the complete lack of "should" in any of the responses. Egocentrism does not a benignity make.
And if I had to choose between that kind of Chinese brainwashing and Guantanamo/CIA black sites, I'll pick the Chinese option.
Patriotism being one example of this type of propaganda -- the idea that some of us are better than others because we were born on one side of a line in the dirt.
And often each system of beliefs has epistemic protection against debunking... for example, religious believers may view debunkers as agents of evil/Satan, while conspiracy theorists may view debunkers as agents working on behalf of the conspirators. In both cases, one has a "rational" reason to be skeptical of (or even outright disregard) any arguments that attempt to undermine one's axiomatic system.
The more a person seeks the opiatic, emotional feeling of fake knowing, the more receptive he is to religion, political brainwashing, conspiracy theories, prejudices, social authority structures, etc.