I think my reply here probably covers some of your post as well. "Bothsiderism" is an interesting term, but when it comes to relationships with people I care about who are convinced they are right, I'm willing to engage them respectfully instead of assuming they are idiots, immoral, or stupid, as I've discussed before.
I don't see it as "dangerous" because people who believe strongly enough about their views are going to do whatever they want. The only path forward I see for any chance of consensus is to have respectful dialogue, even if I don't agree with someone.
I don't think open dialogue is dangerous.
I think not having open dialogue is dangerous. I think shaming, shunning, etc people for their views before having open dialogue with them is dangerous.
This is my way, and I know it's not for everyone. Some prefer to just sever relationships and move on when people are strongly in disagreement. I prefer to respect both sides as to where they are at talk about it.
I respect that; unfortunately, it requires the other person to also be willing to engage. Prisoner's Dilemma.
This isn't entirely hypothetical. A person in my close social circle has recently decided to double down on Trump, Fox News, All Lives Matter, the whole 9 yards, and actively refuses to even discuss or speak about it, going as far as "don't confuse me with facts, my mind is made up." (Nearly a direct quote.) There's really nothing you can do at that point, but people are still dying, so...
This may be a data point for you to know your approach isn't working. People convince themselves of things via biases. Even the most unbiased person, if truthful, will admit this. We like to think the scientific method is without bias, but it is not. It's maybe the best thing we have going but it has limits. Some people need to be connected to relationally before they will ever understand you factually. "People need to know that you care before they care what you know."
This is inefficient, frustrating, and at times annoying. It simply is. No way around it. We can either disconnect and hope for the best, or we can try different approaches which are more relationally based. I'm reminded of the dude who hung out with KKK members and befriended them in order to win them over to his perspective.
Love your enemies.
Everything that frustrates you.
It's a hard call to action and not for everyone, but I do see the value in trying, and I don't think it validates anything or makes things worse. Open, truthful, respectful, dialogue with true humility (not feigned humility where you really know you're right and they are completely wrong) can create results.