API calls failing with create-react-app and node backend in production

So, I am following this tutorial on setting up a front-end/back-end with create-react-app boilerplate:

https://www.fullstackreact.com/articles/using-create-react-app-with-a-server/

The APIs I have set up to be sent to the backend don't work in production mode.

I use this in client/package.json to proxy to the backend:

  "proxy": "http://localhost:8081/",

And I serve up the files like this in production on my node backend:

app.set('port', (process.env.PORT || 8081));
// Express only serves static assets in production
if (process.env.NODE_ENV === 'production') {
  app.use(express.static('client/build'));

  // Always return the main index.html on routes that should return a "page" (e.g. /contact),
  // so react-router will render the route in the client
  app.get('*/:page', (req, res) => {
    res.sendFile(path.resolve('client/build', 'index.html'));
  });
};

But the API calls aren't called properly in production mode. Any idea why?

And secondarily: Will I need to anything special to make it run on an nginx server?

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