Politics is important. What our government does (or doesn't) do can have a huge impact on the well-being of its citizens and the world. So ideally, people would think through the issues rationally, try to learn more, consciously work on identifying/eliminating their misunderstandings/biases, and be interested in discussing their differences of opinion with other educated/rational people in hopes that one or more sides can learn something.
But then there's reality. Sure, people have the capacity to think objectively and skeptically, but on some topics people prefer to think tribally. You just pick a side, usually your "home team" (whatever your parents and/or peers think), and then view everything as a simple good-versus-evil struggle where, of course, your team is always right and the others are always wrong. And of course, you'll want to post stuff on Facebook that displays your team/tribe loyalty... whether or not it's factual or logically consistent is not really important.
If you do hope to learn from the opinions/knowledge of others, the time you devote to that is a limited resource, so you have to choose wisely how to spend it. An important rule of thumb would be to ignore those purely tribalistic people. Which leads me to the shutdown...
Democrats passed a law that Republicans don't like. After not being able to stop it through the accepted means of passing/altering/repealing a law, many Republicans in Congress have decided to shut down the government until they get their way. The details of what "shutdown" means can be read here.
It isn't too often that something happens like this where the right answer is so obvious. This is a terrible, dysfunctional way to run a government. Even if you support the goal of the Republican politicians here, this is such an obviously bad way to do it. If this works, won't this tactic be much more likely to get used again? Should the Democrats think they should shut down the government to get their way the next time Republicans regain a majority and pass a law that they don't like? Regardless of what you think about "Obamacare", there can't be any negotiation on these grounds for the same reason we shouldn't negotiate with terrorists or pay ransoms even when the immediate result of that action seems positive. Giving any legitimacy to that tactic would create long-term consequences worse than the perceived benefits of its first use.
I've seen many people post stuff on Facebook about whether certain national parks/monuments should be closed. And I do think there's room for debate there. The National Park Service has a policy of only having things open if they have sufficient security to monitor them, which they now do not. Maybe that policy should be changed or applied in a more case-by-case basis rather than as a blanket policy. But what's amazing is that many people are presenting this as the outrageous story of the government shutdown and don't have anything to say about the shutdown itself. Really???? What justification could there possibly be for that other than looking for any excuse to criticize Obama and trying as hard as possible to ignore obvious flaws within your "tribe"?
It's mind-boggling, but it's also a win-win situation. They and like-minded people on their "team" get to have their warm, fuzzy (apparently mind-numbing) feeling of tribal unity. And for anyone else this serves as a useful advertisement that states "there is no reason to listen to anything I ever have to say about politics".