Conditionally disabled React Checkboxes

You could keep an object in state that keep track of the checkbox values, and in your render method you can check if there are 2 or more checkboxes that are checked and use this to disable the others.

Example

class App extends React.Component {
  state = { checked: {} };

  onSelectedChange = index => {
    this.setState(previousState => ({
      checked: {
        ...previousState.checked,
        [index]: !previousState.checked[index]
      }
    }));
  };

  render() {
    const { checked } = this.state;
    const checkedCount = Object.keys(checked).filter(key => checked[key]).length;
    const disabled = checkedCount > 1;

    return (
      <div>
        {Array.from({ length: 5 }, (_element, index) => (
          <input
            key={index}
            onChange={() => this.onSelectedChange(index)}
            type="checkbox"
            checked={checked[index] || false}
            disabled={!checked[index] && disabled}
          />
        ))}
      </div>
    );
  }
}

ReactDOM.render(<App />, document.getElementById("root"));
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>

<div id="root"></div>