Does adding vinegar to soup make it spoil faster?
I think it makes no difference as the vinegar does not contain bacterial spores. If so much vinegar that makes the soup significantly more sour then it can eventually go wrong even later as bacteria don't prefer the acidic environment.

To add a concrete quantitative example: while cooking 3 pieces of beetroots I added 5 tsp 6% acetic acid balsamic vinegar. 7 days later kept in fridge (~4C) is still good. I am quite sure it's because the acidity as meals used to go wrong much sooner than 7 days.