Clifford’s rule isn’t self-refuting. There is evidence for it, namely the harms that come from believing on insufficient evidence, which his shipowner parable illustrates.

Fair; Clifford does give a consequentialist argument for his rule. The precise point is that the rule is not believed on the basis of the kind of evidence the rule itself demands, since the argument from harm is a moral argument, not empirical proof that the rule is true. That still shows the rule needs non-scientific support to stand, which is the point. A moral argument for an epistemic rule is a perfectly good thing to have; it just cannot be the only kind of reason allowed.