Well, yes and no. Imagine the opposite situation, where ImaginaryDB is revealed to have made a sweeping genocide possible. I doubt there would be an instant rush to switch DBs, but over time, I would bet many people would use something else. I would like to think that ethics are a part of every human endeavor (we're not quite there yet, unfortunately).
> where ImaginaryDB is revealed to have made a sweeping genocide possible.
Freedom 0 according to the FSF is the freedom to use the software for any purpose (http://www.gnu.org/philosophy/free-sw.en.html). Genocide included. I don't see why that would make anyone switch unless the authors publicly said "yes, we support this genocide".
Software is a tool, plain and simple. A better example right now would be Tor or Bitcoin. People aren't flocking away from those for their use in crimes...