Make sure that your web package has the following:
module: { loaders: [ { test: /\.css$/, loader: "style-loader!css-loader" } ] }
This will require and link any css file that you need, and I would pull them exactly how you did it:
require('react-select/dist/react-select.css');
Another workaround that works for sure is that you copy this css file, and in html you link it by:
<link rel="stylesheet" href="/path/to/react-select.css">
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