We just had a situation where the latest WordPress update actually caused a 403 Site Error for the whole website! So sharing the solution.
After looking into it and working with the hosting company too, we found that an update to the .htaccess file had changed the permissions for the web server.
To fix this, we just added “Options +FollowSymLinks” to the top of the default WordPress .htaccess file and voila! – the site is working again!