This is only as vague as you want it to be. If you want, you can cut the line, based on whatever reason, and call all the starts on one side "red giants" and stars on the other side "white dwarfs". It would be pointless, but there is nothing stopping you.
There is nothing stopping you only in the sense that nothing stops you from asserting falsehoods. (As we see is the case for you personally.)
It is intrinsically vague: "Red giant" does not and cannot have precise boundaries, as is true of all words. The same is true of "White dwarf." If you cut the line, you will indeed be cutting it arbitrarily, as you say yourself, and this has nothing to do with the meaning of those words.
The rest does not respond to the comparison about consciousness, and as I said we won't be discussing the comments on language.
"Red giant" does not and cannot have precise boundaries
Again, you make a claim and then offer no arguments to support it. "Red giant" is a term defined quite recently by a fairly small group of people. It means what those people wanted it to mean, and its boundaries are as precise as those people wanted them to be.
we will not be continuing this discussion of language. Not until you show that it has something to do with consciousness. It doesn't.
You started the language discussion, but I have to explain why we're continuing it? I ...
(This post grew out of an old conversation with Wei Dai.)
Imagine a person sitting in a room, communicating with the outside world through a terminal. Further imagine that the person knows some secret fact (e.g. that the Moon landings were a hoax), but is absolutely committed to never revealing their knowledge of it in any way.
Can you, by observing the input-output behavior of the system, distinguish it from a person who doesn't know the secret, or knows some other secret instead?
Clearly the only reasonable answer is "no, not in general".
Now imagine a person in the same situation, claiming to possess some mental skill that's hard for you to verify (e.g. visualizing four-dimensional objects in their mind's eye). Can you, by observing the input-output behavior, distinguish it from someone who is lying about having the skill, but has a good grasp of four-dimensional math otherwise?
Again, clearly, the only reasonable answer is "not in general".
Now imagine a sealed box that behaves exactly like a human, dutifully saying things like "I'm conscious", "I experience red" and so on. Moreover, you know from trustworthy sources that the box was built by scanning a human brain, and then optimizing the resulting program to use less CPU and memory (preserving the same input-output behavior). Would you be willing to trust that the box is in fact conscious, and has the same internal experiences as the human brain it was created from?
A philosopher believing in computationalism would emphatically say yes. But considering the examples above, I would say I'm not sure! Not at all!