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This uncomfortable feeling must be part of the reason extremists put so much energy into portraying anyone who disagrees with them as an other-side extremist, or at best an intentional moderate (http://paulgraham.com/mod.html ).
If there's another way of disagreeing with them besides being an other-side extremist or intentional moderate, what is it? It must suggest alarming hypotheses when the extremist compares his neatly matching set of opinions with the variegated ones of accidental moderates.
Productive disagreement comes from meeting them at their neurological base and giving them an excuse to travel to yours. Specifically the hippocampus needs enough to agree with before it's able to consider other ideas. Familiarity builds the bridge.
Oversimplifying due to character limits
"What is not surrounded by uncertainty cannot be the truth." -Richard Feynman
It’s pretty clear that many extremist are badly craving for reassurance. Basically climbing Maslow’s pyramid. I think it was Raymond Aron who said « they don’t want to understand the world nor even change it, they want to denounce it »
I agree that thinking from first principles makes a lot of sense. We need much more of that. But I think you're too hard on "extremists"; perhaps generalizing from a view of today's politics to a unified theory.
I suspect the collective views of those fighting for civil rights or women's suffrage, or to end apartheid / communism, etc. were a) way outside the norm and b) quite homogeneous.
There is another way. Don't express an opinion, but mention any inconvenient data and ask difficult what/how questions. Downside is that you're still disagreeing with an extremist. It won't be fulfilling. They get ridiculous or run. It's still not a good use of time & energy.
Frame it differently: you’re an early adopter of a future consensus
This 1945 propaganda piece is especially relevant during these times:https://youtu.be/vGAqYNFQdZ4
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