“There is no nonexisting”? There is no noun, or at least not anything readily understood to be one, only an adjective. To preserve the pseudo-profundity of the original, however, one might write instead:
There exists no nonexisting state.
Now any adjective can be substantivized — the poor, the obnoxiously wealthy, the aesthetically challenged — but only when clearly marked:
In an ideal world, there would be no poor.
I'm not overly fond of this sentence, but because of context and the plural verb, you know I mean poor people, thus grammatically, all is well. So you might come up with the sentence:
The nonexisting exist only as a mental construct.
Now in this deep dive into the intricacies of English grammar, you might have stumbled upon something like this:
Nonexisting does not exist.
Strictly true when nonexisting is in italics or framed in quotation marks to indicate its usage as a word in isolation, this one might survive the last beer at 4 am, but not the first morning coffee. While existing can be used as a noun, nonexisting does not exist as a legitimate English gerund because to nonexist isn't a verb. And that brings us back to your original statement:
There is no [such gerund as] “nonexisting.”
Truer words were never spoken! But to those of us not privy to the beer and coffee, the sentence is utter rubbish.
Not so with your second sentence:
There is no red.
Even without context, you know that among various things in your immediate field of vision there isn't a red one, whether paint, pigment, crayon, or nail polish. Red is a substantivized adjective and immediately recognized as such. Nonexisting isn't.