Keep in mind that neither A nor B will change--only C.
You only use semicolons to join two independent clauses without using a conjunction. For example, the following sentences are both correct and mean the same thing:
- I wanted to play, so I put on my shoes.
- I wanted to play; I put on my shoes.
Because "only C" cannot be treated as an independent clause (it shares a verb with the first independent clause and thus belongs to the first independent clause), you cannot separate it with a conjunction. Therefore, you also cannot separate it with a semicolon.
A dash is a better choice than a comma here, though, because you cannot move the phrase "only C" to a different part of the clause to make it flow better. For example, both of these sentences are wrong:
- Keep in mind that only C will change, neither A nor B.
- Keep in mind that neither A nor B will change, only C.
The comma doesn't do enough work because the clause needs to be completely interrupted and then resumed. Also, you won't find the above examples described among valid uses of the comma.