The definition you quote is interesting since it describes a skeptic who would remain neutral, rather than skeptical, when reacting to non-empirical claims. Such as the existence of God, say - as long as the person is not saying that their belief or assertion is based on empirical claims. I rarely encounter that kind of skeptic.
I don't actually fully support that definition
It's been written very carefully and a little politically. I just copy pasted it a little quickly.
Please note the neutrality bit only applies when claims don't impact the practice of science. It is often the case that belief in Gods does impact the practice of science. I think you will find people are a lot more neutral to beliefs which have no impact on them than ones which do, even if they fundamentally disagree.
Karl Popper came up with a few examples, including Darwinian evolution. His ideas are (inevitably) more involved than the brief mention that was made here. To that I'd add, Behaviourism, String Theory, the Copenhagen Interpretation of Quantum Mechanics. If you're ever heard the theory that people don't really have free will and that all conscious thought is illusion, I'd suggest that was unfalsifiable as well.
Evolution by natural selection is falsifiable, string theory as I understand it is on extremely shaky ground, it's certainly not the consensus of expert opinion (but one day once it has been made falsifiable it could be). Consciousness is a tricky one, I've heard of brain damaged patients who consciously can't detect certain visual stimuli but physically react like they can (on an unconscious level). Also it's pretty clear that humans do a lot of things unconsciously such as pulling your hand away from a hot stove but if required are able to hold their hand against the hot stove and consciously override the unconscious reaction. I'm not saying that is proof but I wouldn't rule consciousness out as being unfalsifiable one day. I guess it depends on how you define consciousness. But if you want a useful definition that makes predictions then you'll need falsifiability.
I'm not really suggesting that all knowledge is falsifiable but perhaps all useful knowledge is falsifiable?
Unknown means unknown.