Should we use a semicolon or comma when an adverbial dependent clause containing a list is followed by an independent clause?
While not everyone is a Newton, Einstein, or Hawking, every one of them is a fascinating character with a unique story.
or:
While not everyone is a Newton, Einstein, or Hawking; every one of them is a fascinating character with a unique story.
First of all, your example sentence as an issue beyond the comma.
The use of everyone clashes with every one of them.
To be grammatical, it needs to be rephrased in one of two ways:
While not everyone is a Newton, Einstein, or Hawking, everyone is a fascinating character with a unique story.
While they aren't all a Newton, Einstein, or Hawking, every one of them is a fascinating character with a unique story.
So, let's assume that the sentence has been corrected to one of those two versions.
In this particular construction, the sentence takes the form while X, Y.
Changing the comma to a semicolon would break that form and lead to confusion. (The while x would be stranded as a sentence fragment.)
On the other hand, if you remove while, you can use a semicolon without a problem—but only if you make some other changes.
For example:
Not everyone is a Newton, Einstein, or Hawking; however, everyone is a fascinating character with a unique story.
They aren't all a Newwon, Einstein, or Hawking; but every one of them is a fascinating character with a unique story.
Note that it is an erroneous belief that you can't start a sentence with but. See the blog post "Can I Start a Sentence with a Conjunction?" by Neal Whitman where this is discussed. Just as a sentence can start with but, so can a sentence continue with but after a semicolon.
