Must we abandon classical logic or a single reality?

Frauchiger and Renner argue that "we are forced to give up the view that there is one single reality."*
Now Fortin and Lombardi argue that quantum propositions have a non-Boolean structure and Frauchiger and Renner were wrong to make use of classical logic in their proof. Specifically, they argue that one can not apply the classical inference rule of transitivity of a conditional when dealing with quantum propositions.** I, of course, have considered abandoning both purely classical logic and a single reality. See my blogs of 2 and 4 November 2018, 1 December 2018 and 1 January 2019.

* "Single-world interpretations of quantum theory cannot be self-consistent," 2016
** "Wigner and his many friends: A new no-go result?", 2019