However a counterexample from my own life: I only learned German starting in my late 20s and when, 10 years later I heard the Matthäus-Passion and could understand the lyrics I wept...and I don't even know much about christianity.
It's actually not true that the "vast majority" of Bach's work had no texts. Bach wrote over 200 cantatas (with around 5-10 movements and separate texts each) plus an assortment of masses and 4 extremely large choral/orchestral works: the St. Matthew and St. John Passions, the Christmas Oratorio, and the B Minor Mass.
Looking at the catalog of all of Bach's works, which I have here, BWV (Bach Werke-Verzeichnis) numbers 1 thru 1071, you get all the way to BWV 525 before you even get out of the vocal works. Numbers 1 thru 524 are all cantatas, masses, oratorios, lieder, the many chorales of course, secular and comic cantatas, etc. And of course many/most of these are far larger than the individual organ works.
(Bach actually wrote a lot more cantatas than this; but only around 224 of them survived. Another hundred or so were lost.)
Which parts made you weep?
Start with "Eli, Eli, lama sabachtani" and "Wahrlich, dieser ist Gottes Sohn gewesen" and "Und von der sechsten Stunde an ward eine Finsternis über das ganze Land bis zu der neunten Stunde" and...see? I can't stop once I get started.
It even begins with him being a bit of a prig as his acolytes express their unhappiness. But then he himself expresses pathos (Meine Seele ist betr ̧bt bis an den Tod, bleibet hie und wachet mit mir.) The story becomes unfair. I really felt the unfairness of his trial.
It's a much more sympathetic story than, say, Plato's recitation of the death of Socrates, who comes off as a jerk.