I’ve found a few related questions, but none that specifically answers this quandary:
"To people like you and I/me—those who face uncertainty, trials, and trouble—the apostle Peter wrote these words."
Without the interjection, "me" would be correct because "you and me" is the object, Peter is the subject. But the interjection makes "you and I" the subject and "uncertainty, trials, and trouble" the object in this sentence within a sentence.
Would the rule be that the interjection does not change the grammar of the surrounding sentence, and therefore I should go with "me"?
(While we’re at it, is the part between the dashes truly called an "interjection"? I’m not sure what else to call it.)
Thanks in advance.
That clause is a "parenthetical". An interjection is
a word or expression that occurs as an utterance on its own and expresses a spontaneous feeling or reaction. It is a diverse category, encompassing many different parts of speech, such as exclamations, curses, greetings, response particles, hesitation markers and other words. Wikipedia
A parenthetical doesn’t usually change the grammar of the surrounding sentence. It’s just being used here to provide additional information about the previous phrase, "people like you and me". The role of that phrase in the sentence is still as the object, so you use "me" rather than "I".
You could potentially rewrite the sentence into two independent clauses, and then make "You and I" the subject of one clause:
You and I face uncertainty, trials, and trouble; the apostle Peter wrote these words to people like us.