For the first part, absolutely. Small children are completely incapable of deciding what is true and what is not true. The power is completely in the hands of the parent.
I also agree that the use of the word “brainwashing” can easily be subjective. Some Muslim parents inevitably think Christians brainwash their kids and vice versa. Agreed. I imagine many Christians are devasted “knowing” that children of atheists are likely to be bound for hell if they don’t find faith on their own.
However, I think acknowledging that the term can be subjective can mistakenly take us down the path towards relativism.
There is more evidence for some things, less for others, and no evidence for some ideas. As such, there are different levels of justification for teaching your children that something is “true” or not.
So although I agree that the term brainwashing is often used by outsiders judging the information other parents (with different belief systems) convey to their kids, I also think that there are means by which it becomes very difficult for outsiders to justify their claim that a given parent is brainwashing their kids.
For instance, If I can demonstrate the validity of what I teach to my kids, then how would any outsider be able to justify a claim that I was brainwashing them?
“Most birds can fly.” says the mother to her daughter.
However, if my neighbour gets his/her children to believe that boys must have their earlobes removed on their 13th birthday because that is what God wants, are we both equally guilty of brainwashing?
If so, then the term brainwashing ceases to really mean anything and does become completely subjective. Hopefully we can keep the term for something more meaningful than that otherwise it ceases to have much use…that which defines everything, defines nothing.