gistfile1.js

var SelectThing = React.createClass({
  
  getInitialState: function() {
    return {
      chosenFirstValue: "",
      chosenSecondValue: ""
    }
  },
  
  updateFirstSelectValue: function(e) {
    var value = $(e.currentTarget).val();

    if (this.state.secondSelectValue == "whatever") {
      // do some logic
    }

    this.setState({
      chosenFirstValue: value
    })
  },
  
  updateSecondSelectValue: function(e) {
    var value = $(e.currentTarget).val();

    if (this.state.firstSelectValue == "whatever") {
      // do some logic
    }

    this.setState({
      chosenSecondValue: value
    })
  },
  
  render: function() {
    var firstSelectItems = this.props.collection1.map(function(item) {
      return <option value={item}>{item}</option>;
    });
    
    var secondSelectItems = this.props.collection2.map(function(item) {
      return <option value={item}>{item}</option>;
    });
    
    return (
      <div class="select-thing">
        <select onInput={updateFirstSelectValue}>
          {firstSelectItems}
        </select>
        
        <select onInput={updateSecondSelectValue}>
          {secondSelectItems}
        </select>
      </div>
    )
  }
})