That's interesting. What is the philosophically equivalent term(s) that more closely align to the scientific/general understanding of the word?
I don't think there's a specific philosophical term for that. It would be tempting to use the term "empiricist" to emphasize the importance of empirical knowledge, but the term "empiricist" carries slightly different connotation in philosophy (so, for example, you'll have debates between "empiricists" and "non-empiricists" who are both pro-science and both believe in the importance of empirical evidence.) Similarly, I sometimes see science-enthusiasts call themselves "rationalists" to emphasize the importance they place on reason and rationality, but "rationalist" also has a slightly different connotation in philosophy.
Without diverting into new-atheist-speak are there similar differentiations of "skepticism" like these to theism/atheism in philosophy? For example is there such a thing as a moral agnostic realist? Surely it can't be that a person is either a realist or anti-realist and nothing in between.
Yes, it's possible to be a realist and skeptic about morality - such a person would believe that there are mind-independent moral facts, but we don't know what those facts are. Whether there's a good reason for having this view is a different question, but it is a view that you could have.
That doesn't seem like it fits the word skeptic - unless it's this stricter non-standard version of philosophical skepticism you mention.
Yes, I'm talking about skepticism in the philosophical sense of the term.
Because someone who denies knowledge of the future would be a future denier (or something similar).
I don't know what that means. A "future denier" sounds like someone who denies that the future exists, which is more of a metaphysical position than an epistemological one.
A skeptic would be more along the lines of: we cannot know for absolute certain what the future holds, but we have probabilities for the future based on the past that, to various degrees, will likely be.
Who said that knowledge has to constitute 100% certainty?
Some moral realist theories claim moral facts exist mind-independently. But as far as I can tell these facts cannot be demonstrated in any mind-independent way.
What does it mean for something to be "demonstrated in a mind-independent way"?
If they can't be demonstrated in such a way what reasons are there to believe they exist, mind-independently?
Well, it depends on the view. For example, you might think that what's moral depends on what maximizes happiness, and perhaps you have no reason to doubt this claim. But you might also think that we're rarely in a position to know which particular actions will maximize happiness. So that's a case where there's no reason to doubt that there are facts of the matter about morality, but we don't know in particular which actions are right or wrong. Alternatively, you might think that there can only be moral obligations or prohibitions if there's a God to command/forbid us from doing certain things, and perhaps you have no reason to doubt this view. But you might also think that we have no means of knowing God's commands (or if there even is a God), so that would be another way of thinking that there are moral facts but not knowing in particular what is morally forbidden or required.
So whether it makes sense to think there are mind-independent moral facts while also being skeptical about the particulars of those facts depends on the circumstances.
Isn't that moral nihilism?
Moral nihilists don't think morality exists. This could be expressed different ways, such as "all moral statements are false" or "nothing is forbidden/obligatory" or "nothing is morally good or bad", etc. That's different from saying that knowledge of right/wrong is impossible.
Incidentally, sometimes "moral skepticism" is used to mean "moral nihilism" (e.g., Mackie called himself a "moral skeptic" in some places.)
Skepticism, at least the general/scientific meaning of the word would merely state that something like: there are is no good evidence to support knowledge of right and wrong and thus there are no reasons to believe it exists. Not necessarily that knowledge of right/wrong is impossible.
That's fine, but the point of my post was to show you why "skepticism" if frowned upon by philosophers, so I was explaining to you how philosophers are using the term when they say that moral skepticism is bad. It wouldn't make sense to ask why moral philosophers don't like "skepticism" and then use that term to describe a position they aren't talking about.
On that face of this scenario doesn't this pre-suppose that immorality exists without having demonstrated it's existence? To be clear I don't doubt that the feeling of immorality exists in most people, I'm just not sure that that feeling (or intuition) somehow proves actual immorality exists in the world.
If I were to ask you whether there are other people in the room with you, and you looked around and said, "Of course there are! I can see and hear them all around me!", I could say to you that you're "pre-supposing that other people exist without having demonstrated their existence". After all, all you have is the perception that other people exist, but how can you be sure that your perception somehow proves actual people exist?
I assume you think this is a rather ridiculous view and that we have no good reason to doubt that that other people actually exist based on our perceptions. Likewise, what good reason is there to doubt that torturing a granny for fun is immoral based on what you call "feelings"?