Which of your positions is not a position?
Take a view you hold strongly. Now state what evidence would move you off it. If nothing would, you are not holding a belief about the world — you are holding a commitment about yourself. Both are legitimate. Confusing them is not.
The distinction is between a claim, which answers to evidence, and a stance, which answers to values. Popper's falsifiability criterion fails as a demarcation of science, but it works surprisingly well as personal hygiene: not as a test of what is true, but as a test of what kind of thing you are saying.
Most arguments that go nowhere are two people trading claim-shaped sentences where at least one is actually a stance. Naming which is which either ends the argument or makes it worth having.
Wittgenstein's point is that doubt needs a fixed frame to operate in. That the world existed before your birth, that your hands are your own — these are not conclusions supported by evidence, they are the conditions under which evidence means anything. Some unfalsifiable commitments are not failures of rigour but the floor the rigour stands on. The work is telling those apart from the ones you are protecting.
The interesting case is not a belief with no possible disconfirming evidence. It is one where you can name the disconfirming evidence fluently, and you know you would not update if you saw it. That is much more common, considerably less comfortable, and not detectable by any test someone else can administer.
The test is too clean, and it quietly favours the measurable.
Plenty of defensible beliefs have no crisp falsifier — most moral positions, most judgements about people, most aesthetic commitments. Demanding one for every view does not produce rigour; it produces a preference for the kinds of claims that happen to come with instruments attached.
A worked account of belief revision that handles value-laden claims without the claim/stance split would make it redundant.