This rules out religion, politics, philosophy and most policy proposals as interesting controversies
And yet there are clearly some rational, truth-seeking experts on each side of many or most of these controversies.
If you can identify people who are rational, domain experts, honest, and incentivized to seek the truth, then I think you should trust them over the broader 'expert' community.
If such people don't agree with one another, then they should make clear why they disagree. If they fail to do this, then either they are not very good at practical rationality, or they aren't trying to make themselves clear to external observers.
If they've made it clear why they disagree, and it's a matter of domain expertise you're not qualified to judge yourself, then you're back to the outside view and head-counting. But I think this is a rare case.
For every controversial subject I've heard of, there are always numerous very smart experts on either side. So I'm curious how it is that rational non-experts come to believe one side or the other.
So, what are your meta-arguments for going with one side or the other for any given controversial subject on which you have an opinion?