I think it really depends on what it is and if you have others that can corroborate your story and will back you up. I do have children in the district, but so far have not really had issues that made me raise eyebrows yet.
The one conflict we did have a few years ago was put to a vote in the district about consolidating schools. We live in a district where several small towns each had a K-6 elementary school and it was decided, against our objections, that each town would have 2 grades and the kids would get bussed to all the different locations etc. The district said it was to save money even though it was a hassle for all of us to send our kids to a bunch of different schools. Ultimately the people in the larger town outvoted and outnumbered us - so we lost. Several parents did move to a different district after that. Sometimes you fight the good fight and lose anyway ;) - I happen to love our home however, and as tempting as it was, I chose to remain here.