React app that receives data via an AJAX requests, display the data and makes it searchable
Looks pretty idomatic :) the one major thing you might want to do is make use of propTypes to more explicitly define your Component API's. PropTypes help set expections for what values should/can be.

For instance in SearchBar your doSearch() method looks like

this.props.change(e.target.value.toLowerCase());


There is an implicit assumption that onChange is never going to be null, and that it's a function. You can codify that (and guard against dumb mistakes) by adding

propTypes: {
  onChange: React.PropTypes.func.isRequired
}


alternatively you can leave off: isRequired and provide a default value for onChange (perhaps a noop function).

In PollList

this line is odd (you also do this in _onChange of View):

this.props.data.map(function(value) {
   var head = value.uuid;
   var body = value.question_text;
   arr.push(&lt;div key={head}&gt;&lt;Panel header={head} key={head}&gt;{body}&lt;/Panel&gt;&lt;/div&gt;);
});


.map() already returns a new array so there is no need to push into the arr either just return the child elements or use a forEach()