Can't request data with web client from parse server

Question

I have an iOS app and a javascript web client. The iOS app is working as expected but with the web client I always get this error message:

Failed to load resource: the server responded with a status of 403 (Forbidden) {"error":"unauthorized"}

As a server I use the parse-server example deployed to heroku. git repo

My config is this:

var api = new ParseServer({
  databaseURI: databaseUri || 'mongodb://heroku_q21****.mlab.com:11382/heroku_q2***',
  cloud: process.env.CLOUD_CODE_MAIN || __dirname + '/cloud/main.js',
  appId: process.env.APP_ID || '****',
  masterKey: process.env.MASTER_KEY || '***', //Add your master key here. Keep it secret!
  serverURL: process.env.SERVER_URL || 'http://****.herokuapp.com/parse',  // Don't forget to change to https if needed
  //javascriptKey: process.env.JAVASCRIPT_KEY || '***', 
  verbose : process.env.VERBOSE || 1,
  liveQuery: {
    classNames: ["GameScore", "Player"] // List of classes to support for query subscriptions
  }
});

It does not matter if I use javascriptKey or not. Same result. As web client I use the test.html of the repo to make simple parse tests.
Can someone tell me what might be wrong?