React Jest causing “SyntaxError: Unexpected token .”

Have a look at the Jest documentation for Webpack integration. The problem is that Jest can’t work with other stuff than JavaScript. So you have to mock all non-JavaScript files you import. The easiest way is to configure a moduleNameMapper in your Jest configuration.

{
  "jest": {
    "moduleNameMapper": {
      "\\.(css|scss)$": "<rootDir>/__mocks__/styleMock.js"
    }
  }
}

With a __mocks__/styleMock.js, that looks like this.

module.exports = {};