Obvious example is my understanding of how God is literally in conscious control of every quark and raindrop. There is no way I can assemble data to support that belief.
If you can't assemble data to support an assertion then you could assert anything you like and justify acting on it. I'm sure I don't need to explain to anyone how that can, and has, and still does, lead to disgusting and harmful behavior. Requiring data to support an assertion is a powerful tool in keeping the crazies from the door. History shows us what happens when lots of people accept assertions without asking for good supporting data.
Moving on... well, kinda on a related note...
Metaphysical discussions tend to quickly move towards trying to prove whether a particular assertion is true/correct. And that is certainly my instinct. But I also quite like the idea of focusing instead on whether or not an assertion is
useful, and
where the information comes from. And I think perhaps that's enough to allow us to make an informed decision about whether to accept an assertion and let it inform our behaviour, without having to prove or disprove it definitively.
Newton's laws of gravity are incomplete but they are still useful in all sorts of construction and engineering situations, so we still teach his equations and they are still used to build bridges. Aristotle - not so much - his assertions about gravity didn't prove to be very useful at all so we no longer pay them much attention. So can we say Newton's model is correct? No, because you can't use it to build a satellite navigation system. For that you need Einstein. Newton's work is useful for bridges but not useful for satellites.
Additionally, the simple question "Where are you getting that information from?" is extremely powerful. If the answer is "My parents always told me it's true" then that might not be quite as convincing as "400 different experiments have been conducted over the last 300 years and every single one verified the same result, and every experiment was carefully documented and has been repeated by others 7000 times and the same results were replicated, and you could go replicate the experiments yourself if you wanted to, and 60 other major theories in related fields also predict this same result to an accuracy of 42000 decimal places." In neither case do we need to actually prove whether the assertion is correct. If the answer is the former, I will feel very comfortable dismissing it as hearsay and not acting on it; if the answer is the latter, I will feel very comfortable assuming that it is in fact correct and letting that knowledge inform my behaviour. Also in both cases I can keep my mind open to the fact that I might be wrong to dismiss or accept the assertion, while still getting on with my life knowing that I did the responsible thing and at least asked for some supporting data before acting.
I've used physical examples but the same would work for metaphysical. I haven't been able to find any credible data to support the idea that there's an afterlife of any kind, and that includes an afterlife in which I'm judged on my actions in this life. I don't need to prove it one way or another, I just need to decide whether to behave today as if I'm gonna be judged or not. Is the assertion useful to me - well, yes, I think it would make a huge difference. If I really felt that I was gonna be judged, I'd have a heap of questions such as what actions are acceptable to this judge and which aren't, and I would definitely act accordingly. So then I have to ask whoever's making the assertion - where are you getting that information from. And when they say "I just know it to be true, it's not possible to find any data to support it" - then at that point I feel comfortable in dismissing it. They may well be correct, but without supporting data I don't feel like I can justify behaving as if they are.
I wonder whether focusing on those two things can help to avoid a lot of the conflict that arises when discussing, well, anything, but certainly metaphysics.
Of course it doesn't avoid the conflict that arises when people act on assertions (provable or not). But anyway, I find it an interesting way to look at it, and often it's the best I can do at the time in order to make a decision: alright, that's what you're claiming but i) is this at all useful? and ii) where are you getting your information from?