@li-an and @facter:
If disabling the parallel option fixes it, try this to find out why:
Disable all plugins except EWWW IO. Upload an image, and see if it gets optimized (give it a few minutes, since it is working in the background). Or you can try optimizing one of the ones you’ve uploaded in the last few weeks.
If that works, then reactivate plugins one by one and try uploading/optimizing an image until it breaks again.
If it doesn’t work, also switch to one of the default themes to see if your theme is interfering with EWWW’s new background/parallel optimization.
If none of that works, check with your webhost to see if they have something blocking the plugin from using async requests to admin-ajax.php.