Lukas,
When you deactivated Root and Admin protecting your are turning off BPS. So your problem is somewhere else.
Assuming your not using any “Caching” plugin like Wp-SuperCache, W3Total Cache because they can cache AJAX if not setup correctly. Also 3rd party database caching will cause issues. You might also check with your Hosting Tech if they enabled some type of Server Caching.
Before you get started make sure that your browsers on your computer and your JavaScript is ALL up to date. Download and install Mozilla and Google Chrome. Download and install CCleaner to erase your browser caching.
As mentioned above, switch themes and deactivate ALL your plugins. One of them is conflicting with WooCommerce. More than likely its a badly written or not updated plugin’s java that is conflict with WooCommerce Add To Cart Java.
What you are doing is switching to a default theme like the twenty-one theme and the ONLY plugin activated should be WooCommerce. Now check if the Add to Cart works.
If it doesn’t, go over to the support forum of WooCommerce. WooCommerce requires that PHP sessions paths are saved to a tmp folder. Its a php.ini setting with the session.save_path that has to be set to /tmp
If it does work, activate your Custom Theme and Test the Add To Cart. Then activate your plugins one by one till you find the problem.
Good luck.