How to disable form submit button until all input fields are filled?! ReactJS ES2015

I would take a little bit different way here...

Instead of setting submitDisabled in every single onChange handler I would hook into lifecycle method to listen to changes.
To be exact into componentWillUpdate(nextProps, nextState). This method is invoked before every change to component - either props change or state change. Here, you can validate your form data and set flag you need - all in one place.
Code example:

componentWillUpdate(nextProps, nextState) {
  nextState.invalidData = !(nextState.email && nextState.password);
},

Full working fiddle https://jsfiddle.net/4emdsb28/

Here is a basic setup for form validation:

getInitialState() {
    return {
      email: '',
      text: '',
      emailValid: false,         // valid flags for each field
      textValid: false, 
      submitDisabled: true       // separate flag for submit
    }
  },
  handleChangeEmail(e) {         // separate handler for each field
    let emailValid = e.target.value ? true : false;        // basic email validation
    let submitValid = this.state.textValid && emailvalid   // validate total form
    this.setState({
      email: e.target.value
      emailValid: emailValid, 
      submitDisabled: !submitValid
    })
  },
  handleChangeText(e) {         // separate handler for each field
    let textValid = e.target.value ? true : false;        // basic text validation
    let submitValid = this.state.emailValid && textvalid   // validate total form
    this.setState({
      text: '',
      textValid: textValid, 
      submitDisabled: !submitValid
    })
  },
  render() {
    return <div>
      <input name="email" value={this.state.email} onChange={this.handleChangeEmail}/>
      <input name="text" value={this.state.text} onChange={this.handleChangeText}/>
      <button type="button" disabled={this.state.submitDisabled}>Button</button>
    </div>
  }
})

In a more elaborate setup, you may want to put each input field in a separate component. And make the code more DRY (note the duplication in the change handlers).
There are also various solutions for react forms out there, like here.