Replacing the drawn-out opening phrase with the standard modern date equivalent gives us this:
That on January 1, 1863, all persons held as slaves within any State or designated part of a State, the people whereof shall then be in rebellion against the United States, shall be then, thenceforward, and forever free:
As the Wikipedia article on the Emancipation Proclamation points out, President Lincoln had issued the preliminary proclamation declaring his intention to emancipate (as Wikipedia puts it) "all slaves in any state that did not end its rebellion against the Union by January 1, 1863." The actual Emancipation Proclamation was issued the day it took effect (January 1, 1863), which means that the prospective wording of the sentence that the OP asks about ("the people whereof shall then be in rebellion ... shall be then, thenceforward, and forever") might at that point have been reframed in simple present tense:
That as of today, January 1, 1863, all persons held as slaves within any State or designated part of a State, the people whereof are in rebellion against the United States, are now, and forever more, free:
This is in fact essentially what Lincoln did in the actual Emancipation Proclamation, first quoting the older language and then saying this:
And by virtue of the power, and for the purpose aforesaid, I do order and declare that all persons held as slaves within said designated States, and parts of States, are, and henceforward shall be free; and that the Executive government of the United States, including the military and naval authorities thereof, will recognize and maintain the freedom of said persons.
Returning now to the preliminary proclamation, we can also alter the wording "the people whereof" to the simpler (and equivalent) "whose people":
That as of today, January 1, 1863, all persons held as slaves within any State or designated part of a State whose people are in rebellion against the United States are now, and forever more, free:
This last alteration should remove any possibility of misreading the intent of the sentence in the way that (according to the OP) it "might be read by some to indicate that a state which holds slaves is to be considered 'in rebellion against the United States.'" But it seems to me that the original wording can't be interpreted to mean that a state permitting slavery is on that basis alone to be considered "in rebellion" under the original wording of the Emancipation Proclamation in any case.
Such an interpretation hinges on reading the word that in the phrase "the people whereof shall then be in rebellion" to mean "therefore." But that reading blows up the logic of the sentence, since logically "therefore" requires a prior assertion or proposition or condition precedent to provide the basis for the conclusion—and "all persons held as slaves within any State or designated part of a State" isn't an assertion, proposition, or condition precedent; it's simply a lengthily modified subject built around the noun persons.
Syntactically, the phrase "the people whereof shall then be in rebellion against the United States" modifies "any State or designated part of a State." I don't see any other reasonable way to interpret the words. So if the citizens of Western Pennsylvania had chosen December 31, 1862, to engage in a fresh outbreak of the Whiskey Rebellion of 1791, those counties would logically have fallen under the terms of the Emancipation Proclamation, and any person held as a slave there—perhaps by a Maryland plantation owner who happened to be on a visit to friends in Pittsburgh with one or two slaves in attendance—would, as of January 1, 1863, be free under the terms of the Emancipation Proclamation—the slave owner's usual rights under Dred Scott v. Sandford notwithstanding.
Further, I don't see any way to transform the plain meaning of "any State or designated part of a State" into "any State or designated part of a State that permits ownership of slaves." So in my opinion, the proposed interpretation of the quoted sentence in the preliminary Emancipation Proclamation is not semantically defensible, and a reading of the sentence that, in effect, replaces the first then with therefore is not grammatical.