Pass setState functions instead of objects.

example.jsx

import React from 'react';

class Example extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
      thingOne: null,
      thingTwo: null,
    }
  }

  handleChange = ({ target }) => {
    const key = target.name;
    const value = target.value;

    this.setState(() => ({ [key]: value }));
  }

  render() {
    return (
      <form>
        <input name="thingOne" onChange={this.handleChange} value={this.state.thingOne} />
        <input name="thingTwo" onChange={this.handleChange} value={this.state.thingTwo} />
      </form>
    );
  }
}

With babel-plugin-transform-class-properties you can take advantage of => to bind this for you.