As of React 16.2.0, you can add a line like this to your webpack configuration:
new webpack.DefinePlugin({
'__REACT_DEVTOOLS_GLOBAL_HOOK__': '({ isDisabled: true })'
}),
If not using webpack you can put, somewhere in a module imported before react:
window.__REACT_DEVTOOLS_GLOBAL_HOOK__ = { isDisabled: true };
This disables all logs about React DevTools.