ReactJS onClick setState to different element

Only react components have setState method. Working example:

import React from "react";
import ReactDOM from "react-dom";

export default class Nav extends React.Component {
constructor() {
  super();

  this.state = {
    navStatus: "navHide"
  };

  this.navClose = this.navClose.bind(this);
  this.navOpen = this.navOpen.bind(this);
}

navClose(e) {
  e.stopPropagation();
  this.setState({
    navStatus: "navHide"
  });
}

navOpen() {
  this.setState({
    navStatus: "navShow"
  });
}

render() {
  return(
    <nav onClick={this.navOpen}>
      <div id="myNav" className={this.state.navStatus}>
        <div className="navClose" onClick={this.navClose}>
          <object
            className="navCloseBtn"
            type="image/svg+xml"
            data="svg/close.svg"
          ></object>
        </div>                  
      </div>
    </nav>
  );
}

Also you should bind event handlers in constructor instead of render method.

import React from "react";
import ReactDOM from "react-dom";

export default class Nav extends React.Component {
constructor() {
    super();
    this.state = {navStatus: "navHide"};
}

navClose() {
    var navOpened = document.getElementById("myNav");
    this.setState({navStatus: "navHide"});
}

navOpen() {
    this.setState({navStatus: "navShow"});
}

render() {
    return(
        <nav onClick={this.navOpen.bind(this)}>
            <div id="myNav" className={this.state.navStatus}>
                <div className="navClose" onClick={this.navClose.bind(this)}>
                    <object className="navCloseBtn" type="image/svg+xml" data="svg/close.svg"></object>
                </div>                  
            </div>
        </nav>
    );
}
}