Preact with styled-components causes error in browser console

Simply importing styled-components leads to this error in the browser console:

styled-components.browser.esm.js?face:1670 Uncaught TypeError: (0 , _react.createContext) is not a function
    at Object.eval (styled-components.browser.esm.js?face:1670)
    at eval (styled-components.browser.esm.js:2490)
    at Object../node_modules/styled-components/dist/styled-components.browser.esm.js (vendors~index.js:167)
    at __webpack_require__ (index.js:79)
    at eval (index.js?12d5:2)
    at Object../src/index.js (index.js:165)
    at __webpack_require__ (index.js:79)
    at checkDeferredModules (index.js:46)
    at index.js:152
    at index.js:155

I'm using webpack, preact, Babel.

Code to reproduce is literally just this, in a new, empty build:

src/index.js:

import { h, Component, render } from "preact"
import styled from "styled-components"

package.json:

{
  "name": "App",
  "version": "0.0.1",
  "description": "Web app.",
  "main": "index.js",
  "scripts": {
    "build": "rm -rf dist/* && NODE_ENV=development webpack -d --config webpack.conf.js --env development"
  },
  "devDependencies": {
    "babel-core": "^6.26.3",
    "babel-loader": "^7.1.5",
    "babel-plugin-transform-react-jsx": "^6.24.1",
    "babel-preset-env": "^1.7.0",
    "babel-preset-react": "^6.24.1",
    "html-webpack-plugin": "^3.2.0",
    "preact": "^8.4.2",
    "preact-compat": "^3.18.4",
    "styled-components": "^4.1.3",
    "webpack": "^4.28.4",
    "webpack-cli": "^3.2.1"
  },
  "dependencies": {}
}

webpack.conf.js:

const path = require("path")
const webpack = require("webpack")
const htmlWebpackPlugin = require("html-webpack-plugin")

module.exports = {
  entry: {
    index: "./src/index.js"
  },
  module: {
    rules: [{
      test: /\.(js|jsx)$/i,
      use: {
        loader: 'babel-loader',
        options: {
          presets: [
            'babel-preset-env',
            'babel-preset-react'
          ],
          plugins: [
            [ 'babel-plugin-transform-react-jsx', {
              pragma: 'h'
            }],
          ]
        }
      }
    }]
  },
  output: {
    publicPath: ("http://your-hostname.com/"),
    path: path.resolve(__dirname, 'dist'),
    filename: '[name].js',
    chunkFilename: '[name].js'
  },
  optimization: {
    splitChunks: {
      chunks: 'all'
    },
    occurrenceOrder: true
  },
  plugins: [
    new htmlWebpackPlugin({
      template: './public/index.html',
      filename: 'index.html'
})
  ],
  resolve: {
    alias: {
      'react': 'preact-compat',
      'react-dom': 'preact-compat'
    }
  }
}

Build using npm run build works fine, but visiting the resulting page in the browser produces the above error.

Any pointers would be very gratefully received.

Edit:

According to this issue logged against Preact-CLI, preact does not have react's contextApi so I should downgrade styled-components to v3 instead of v4. Downgrading does indeed seem to resolve the issue.

Confusingly though, Jason Miller, author of preact, says in a tweet that "preact supports context just fine". I'm probably misunderstanding this.