There is a difference between opinions and beliefs. One can reasonably argue about the best way to improve the economy for most citizens in a reasonable way (at least with most people). But other issues can’t be argued that way (hard to be specific without violating the TOS), because the position is based on beliefs or worldview, not solely on facts.
Like doschicos I believe in science and facts (but also have political opinions on things that can’t be argued that way). There are those on both sides of some issues that refuse to believe in scientifically verified facts. When I hear people repeating inaccuracies or alternate facts, I find it hard not to try and explain, but it is usually a lost cause. I have given up in the office, as there is no hope. I recently had a great discussion with a middle school family member while hiking who had ventured into some alternate fact websites and was spouting arguments for why the earth might be flat. We were able to refute many of his “facts” and in the end he was at least 90% convinced.
I believe, however, that there should be political discussion at the family table, as I think kids need to be taught how important it is to think about and form opinions on politics. I disagree with those who say these things do not impact our lives - that may be true for a lucky few, but for many people laws and regulations have a direct impact on their lives and livelihoods.
Of course there has to be a line. At our table we tend all be on the same side although some are more extreme than others. And there is one person who does not feel/think the same way. When that family is present, we tend to not discuss the issues all at once, but off to the side. I have shut things down when it is my table, either when the extremists are too loud or when it just gets boring to go over and over the same things, even when we agree.