beneficial bacteria are tolerant of acidic environments (yogurt/pickles/kimchi), and while a bulk of them die in the stomach some do get through. we know this because eating probiotic rich foods regularly does result in a measurable difference in the populations of those specific bacteria in the gut (as long as you continue consuming them).

Eating yoghurt and fresh fruit to replenish gut bacteria has long been common medical advice after severe-diarrhea illnesses. Something does indeed get through.