IT IS SOLVED. The code was ok, the problem was with improper import.
It is a long post (due to code samples). I'll appreciate your patience and will be very thankful for your help!
We have a RoR back-end and React on the front-end and we are using alt as an implementation of flux. We also use babel to compile ES6 to ES5. So the problem is that I can not render component due to 2 errors.
First is Uncaught TypeError: Cannot read property 'map' of undefined
It appears on the render function of MapPalette component:
render() {
  return (
    <div>
      {this.state.featureCategories.map(fc => <PaletteItemsList featureCategory={fc} />)}
    </div>
    );
}
And the second is Uncaught Error: Invariant Violation: receiveComponent(...): Can only update a mounted component.
So here is the whole MapPalette component
"use strict";
import React from 'react';
import PaletteItemsList from './PaletteItemsList';
import FeatureCategoryStore from '../stores/FeatureTypeStore';
function getAppState() {
  return {
    featureCategories: FeatureCategoryStore.getState().featureCategories
  };
}
var MapPalette = React.createClass({
  displayName: 'MapPalette',
  propTypes: {
    featureSetId: React.PropTypes.number.isRequired
  },
  getInitialState() {
    return getAppState();
  },
  componentDidMount() {
    FeatureCategoryStore.listen(this._onChange);
  },
  componentWillUnmount() {
    FeatureCategoryStore.unlisten(this._onChange);
  },
  render() {
    return (
      <div>
        {this.state.featureCategories.map(fc => <PaletteItemsList featureCategory={fc} />)}
      </div>
      );
  },
  _onChange() {
    this.setState(getAppState());
  }
});
module.exports = MapPalette;
FeatureCategoryStore
var featureCategoryStore = alt.createStore(class FeatureCategoryStore {
  constructor() {
    this.bindActions(FeatureCategoryActions)
    this.featureCategories = [];
  }
  onReceiveAll(featureCategories) {
    this.featureCategories = featureCategories;
  }
})
module.exports = featureCategoryStore
FeatureCategoryActions
class FeatureCategoryActions {
  receiveAll(featureCategories) {
    this.dispatch(featureCategories)
  }
  getFeatureSetCategories(featureSetId) {
    var url = '/feature_categories/nested_feature_types.json';
    var actions = this.actions;
    this.dispatch();
    request.get(url)
           .query({ feature_set_id: featureSetId })
           .end( function(response) {
             actions.receiveAll(response.body);
           });
  }
}
module.exports = alt.createActions(FeatureCategoryActions);
And the last - how I render React component.
var render = function() {
    FeatureCategoryActions.getFeatureSetCategories(#{ @feature_set.id });
    React.render(
      React.createElement(FeatureSetEditMap, {featureSetId: #{@feature_set.id}}),
      document.getElementById('react-app')
    )
  }
 
     
    