Parents should let their kids come into their own political views.
Growing up as the child of two educators, I was never told what to think on political matters. I was taught to approach every subject with kindness, love and curiosity, and that my parents would love me no matter where I landed on an issue. If I brought up a political subject in conversation, they would send me to the (shiny new) Internet to research the issue until I could cogently argue both sides. Once I could, they would play devil's advocate to any points I hadn't covered. At the end of this round, I would state my newly formed position on the subject and they would tell me theirs.
It's a lot more work for both the parents and the kids to go through all of these steps, but it can ignite a passionate curiosity about the political system and the issues that now divide it. As kids get older, the tendency is often to adopt the views and practices that are most diametrically opposed to their parents' for the sake of being contrary. The interactive approach can help to strengthen family ties by opening the channels of conversation and giving parents the chance to teach their kids by example.
I can also say that my political views have shifted a little from when I was younger, but they are still deeply rooted in that foundation of love and kindness. I can also say that my parents and I disagree on some issues, but it's been the source of conversation instead of tension in our relationship. It's also taught me how to keep a level(ish) head during the mudslinging of election cycles and focus on the importance of civilized debate. Although our elected leaders might not seem capable of this level of discourse, there is no reason why we should let our homes follow suit.