The logic behind teaching your child what you think is right could be applied to something entirely unrelated to religion but still entirely related to this topic right?
For instance, if a parent taught their children to grow up and murder people, you could sort of categorize that in the same place as teaching your children religion, but only in the aspect that it's the parent teaching their children what they believe to be correct.
In the society we live in, raising someone to grow up and murder people would without a doubt be considered unacceptable. Would that be considered brainwashing? If so, then in the sense that parents teach their children their religion wouldn't THAT be brainwashing?
It's true that we take on our beliefs from outside sources, but I think there's a line between being told something and then having it asserted to be true, or being told something and then making the decision yourself whether to believe it.
If you tried to convince a mentally stable 20 year old man to go outside and just stab someone with a knife it would be highly unlikely to occur because he's already put that outside his area of morality. However, if you assert that the right thing to do is grow up and go outside and stab people to a 6 year old, it would be difficult for them to make the decision on whether or not that is correct or incorrect.
I think the actual topic shouldn't be specifically focused on brainwashing in terms of religion because brainwashing used in that context could really be applied to anything and everything... Society brainwashes us, in fact, to conform to social norms.
As for parents' role in the development of their child, if they were never arrested for a string of murders and they killed people they believed needed to be killed, then there isn't really a way other than your own internal conscience to disprove the fact that it isn't somehow beneficial or "correct". And your own conscience isn't really a factual way to disprove anything at all.
Did I totally get off track or did I cover the topic at least somewhat?