The whole thing? No, the tome is a slog to get through, but at the bare minimum I would expect an educated Christian to have read Genesis, Exodus, parts of Joshua, Samuel, and Kings; Job, parts of Psalms, Proverbs, and Ecclesiastes; the Song of Songs; all of: Matthew, Mark, Luke, and John; Paul's letters, particularly Romans, 1st and 2nd Corinthians, and Revelation; in addition to probably Augustine's Confessions and parts of The City of God. Maybe other works like parts of Thomas Aquinas's corpus, maybe parts of Erasmus's Enchiridion of the Christian Soldier, some of Luther's/Calvin's/Melanchthon's core works if they're Protestant.
MW: don't bother with the whole of Dante's trilogy. If we're just focusing on maximizing cultural/tropic consumption, you really only need to read Inferno. Purgatorio and Paradiso are nice, but they aren't really widely-referenced unless you're running in really academic circles of Medieval Lit specialists.
More recommendations: Candide, seriously. It's short, it's a super quick read, and Voltaire is one of the 5 or 6 most influential western writers of the modern era. Again I'll repeat my recommendation of Augustine's Confessions. The core Medieval fiction texts: The Song of Roland, The Canterbury Tales, Das Niebelunglied (especially if you're into Tolkien - this is a good one), Tristan and Isolde, and Don Quixote (a tome, but one worth reading, imo). I will once again reiterate that reading the core texts of Dickens's, Austen's, and Shakespeare's respective corpora are going to give you the most bang-for-your-buck in the English speaking world.
100 Years of Solitude is also a really good one to read. And again, I'll reiterate: Goethe's Faust and Mann's Der Zauberberg (The Magic Mountain). If we're purely going with culture signalling for academic crowds, Madame Bovary, or much of anything by Flaubert would be worth checking out. Academics in the Humanities disciplines friggen adore Flaubert, and rightly so. And again, if we're going purely for demonstrating erudition among academics, I don't really think that's at all possible without at least superficially familiarizing yourself with the works of Foucault. At the very least, Discipline and Punish is a must-read.
In the end, though, if this is purely a matter of maximizing cultural erudition in the least amount of time, I'd say consuming core cinematic and operatic texts would be the most efficient way of doing so. You can watch 10 great French New Wave, Silent, or Japanese/Italian/Indian films in the time it takes to you read one of these books people are recommending, and you'll appear just as sophisticated in doing so.