Here’s a simplified version of the sentence I'm working on.
Despite what he believed — or thought he believed — he still had to contend with the truth.
Or should I use commas?
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There is no rule that prohibits the use of or to isolate clauses in your interrupting phrase:
A word group (a statement, question, or exclamation) that interrupts the flow of a sentence and is usually set off by commas, dashes, or parentheses.