React - ul with onBlur event is preventing onClick from firing on li

Try using onMouseDown instead of onClick.

The point is the onBlur is triggering a re-render which seems to lead the browser to do not follow up with the onClick: https://github.com/facebook/react/issues/4210

But if you check the onBlur event you can find some info about what's happening, event.relatedTarget is populated and you can use these info to detect when the onBlur is actually triggered by the onClick and chain whatever you need to do.