First of all, I think it was absolutely great that you had both parties in your home.  That taught you to think for yourself probably more than you even realize.  It showed you that people had differences and that was okay.  I am an independent thinker and so are my two children.  I am a Christian, and often my Christian friends do not agree with me.  When my children were younger and trying to find themselves, often their thoughts and ideas did not reflect mine or the way they were taught.  At those times, we discussed these issues but I left it open that they had to decide.  The major issues that were far out came back in line in time.  I truly wanted them to know for themselves, not be robots or do as I do.  The result is they are both strong and analytical.  I have always felt it is all right to agree to disagree.  Your post today is open minded and I like that.

I think that no matter how much parents would like their kids to follow in their thinking, there are too many other factors and influences out there that they will be indepedent thinkers no matter what. Well, I guess that would be most true here in the America. A lot of other countries seem to be more family-oriented, and the children usually will go with what the parents will teach them.

You talk of political and what you grew up with which was invaluable to whom you are now. But independent thinking must cover every aspect of life too. Exposure to many ways of looking at things, the ads that are thrown at them constantly and how they are presented where toys, clothing, gadgets, food, etc. are concerned. Get them to ask questions about everything around them, and look for many answers, be it the library, the internet, or any other resource you can find. There is no one answer and they will learn to choose what is right for them.

@FUNKIEFAIRY@xanga - Hah I know what you mean. I've had political beliefs (opposite from my parents!) since I was nine and while they're both fiscal republicans they pretty much let me make my own decisions and we get in political arguments all the time. My dad was a major prompt in this and when I was 7 and 8 he would sit me down and have me watch the news- then ask what I thought. I'm glad I was raised so opinionated. ^_^ Though I will say that it becomes a problem when I start to argue with my teachers. 

@tortallcit@xanga - I got into some pretty big arguments both with teachers and my peers at an early age about the things I had watched on the news. I think it has made me a better person. I don't let others talk me into doing things I don't want to do or will regret later. I have avioded many of the problems most of my friends have had and I think that the way my parents raised me had a lot to do with that.

I think its part of the responsibility of the parent to give your children a proper religious upbringing. So, its not unexpected that some political views are attached to this, given the state of churches in America today (some people confuse the pulpit with a political podium.)  

@mamabutterfly - It was meant to suggest whether you would encourage your children to think differently than you do, and that your way of thinking is not the "only" or "right" way.   I think the first commenter did a very good job of getting at what I was trying to describe and the way in which she raised her children.

i don't believe independent thinking is what we should be striving for since it is extremely difficult to separate us from society since we are connected in so many ways.  what my wife and i hope to pass on to our children is critical thinking.

consists of mental processes of discernment, analysis and evaluation. It includes possible processes of reflecting upon a tangible or intangible
item in order to form a solid judgment that reconciles scientific
evidence with common sense. In contemporary usage "critical" has a
certain negative connotation that does not apply in the present case.

Though the term "analytical thinking" may seem to convey the idea more accurately, critical thinking clearly involves synthesis, evaluation, and reconstruction of thinking, in addition to analysis.

How to teach?  well, many ways, but that would be too long of a response.