More correctly would we say that we currently have no natural explanation. Under what circumstances can we say call it and say there is no natural explanation?
I wonder if this might be a bit too strong.
Setting any Dawkins-style approach aside, might a better way of putting this be that, up until this point, nothing has been reliably established as supernatural? (let’s use this vexed word as a placeholder, we all understand what it means)
Sure, we could say that the existence of something supernatural may be inferred from a particular argument or set of inferences. We might even have some reasoning that requires us to revise our assumptions about naturalism’s current explanatory power, but does this prove the supernatural, or simply require us to rethink what naturalism might mean?
You talk about moving the goalposts, but isn’t this a pejorative framing? Isn’t the job of science to move goalposts - to provide tentative theories that best explain reality, which may be superseded when new information comes along? Wouldn’t we expect views of naturalism or physicalism to evolve over time? The example of illness being caused by demons before we understood bacteria is a salient one. We tend to have moved from ignorance and often dangerous practices to knowledge and successful interventions.
In all this I’m not saying that physicalism makes perfect sense or is unassailable, or that there is some fixed thing called reality that can be known independently of the human conceptual frameworks through which we make sense of the world.
I do wonder how useful the endless metaphysical speculation about the nature of reality and the search for the really real actually is. What does it bring us, and what difference does it make to our lives?