You don't have to agree with everyone. In fact, the idea that you would is absurd. Throughout life you'll encounter people who have radically divergent backgrounds, experiences, and values. For over 15 years I lived abroad and interacted with hundreds of people across Europe, Asia, and Africa. Their perspectives differed from mine far more often than not, and that shouldn't be surprising. Yet I also found that the vast majority shared certain commonalities: curiosity about the world and other cultures, a sense of humor, a willingness to learn, and basic empathy.
Throughout those years I never experienced culture shock, even in places radically different from my home in rural Wisconsin. I felt it upon returning to the United States once again. The vitriol, division, and unvarnished hate came as a shock. I believe much of it derives from an inability to disagree and debate civilly using facts and evidence, and from mistaking hyper-skepticism for healthy critical thinking. That in itself shouldn't be a surprise either, as this very site came about because of a man who openly and repeatedly professed a belief in "harmless hyperbole" and "alternative facts" while denigrating other sources of information other than himself.
I'm not a conservative. I'm also not a liberal. My views sometimes align with George Will, Vivek Ramaswamy, and Timothy Carney. They sometimes align with Paul Krugman, Barack Obama, and Fareed Zakaria. Until we recognize that we all have multifaceted views that span the political spectrum, we'll never take the first steps necessary to heal our country. We can disagree, but you'll get nowhere if you don't have a foundation for your arguments.
Graham's Hierarchy of Disagreement
In 2008 Paul Graham created this hierarchy to help authors and readers in the digital age better understand how to engage one another with evidence rather than insults. Too often people attempt to argue by calling their opponents names or attacking their sources. Only rarely do you find someone engaging at a higher level in the wild west of the internet.
Read and ensure that you understand what someone is saying. Identify the key points and thesis underpinning their words. Research the issues, and learn to distinguish between reliable sources and those that may have a particular slant (which notably doesn't necessarily disqualify them from being right at times) to support your arguments. And if you find yourself responding with an insult or by attacking the source of information rather the addressing the claim itself, understand that you've already lost the debate.
Resources
It's easy to start an argument when you think you know what you're arguing for...but what if it's not what you actually believe? Rather than seek to understand the diversity of views we each hold as individuals, we put others and even ourselves into boxes. ISideWith is a fantastic site that quizzes you across a broad range of issues and shows where you align to every candidate. Even better, it compares your positions to historical candidates as well, allowing you to get a sense of the politicians and parties you agree with, past and present.
National Institute for Civil Discourse: Engaging Differences
The first and most important step to learning how to disagree and debate more effectively has nothing to do with your arguments. It's learning to reign in your desire to be right and instead developing the characteristics that will help you better understand your opponent and more effectively respond to them: listening, empathy, and similar traits. If we aren't able to learn how to overcome our differences in this nation, we'll continue on the self-destructive path of division, anger, and violence.
Learning to identify credible sources in our modern world is crucial, but actually seeing if you can do it is even better. This quiz will give you a sense of how well you recognize key aspects of credibility.
Contrary to the claim that all mainstream media is "fake," many news organizations are still highly trustworthy. AllSides is a wonderful resource to check the background and political leaning of all major sources, from Fox News to CNN and more.
The Foundation for Critical Thinking
If you want to become a more critical thinker, it takes practice like everything else in life. The Foundation for Critical Thinking offers a vast number of resources to help you get started on that path.
Internet Encyclopedia of Philosophy: Fallacies
Fallacies, errors in thinking, occur constantly in public discourse. This site provides excellent summaries and examples of most fallacies to help you avoid them. Just be aware that the use of certain fallacies doesn't automatically entail that an argument is wrong.