HN user
Whoops. That you would condemn a perfectly reasonable comment like that speaks volumes about your character and the political leanings of whomever is paying for your coffee.
Applications of set theory: all math.
But no, seriously, it depends on what kind of set theory you're talking about. The stuff Hilbert was arguing about up to the stuff still being argued about today in the ivory tower? No, you pragmatically do not need to know that unless you're pursuing a research career in pure math. The stuff in an undergrad probability course? Yeah, sets come up basically everywhere if you're looking and are willing to think like that.