If you have both of them activated, custom post types added to the navigation menu will have weird links. E.g. the actual link is /en/my-ctp/mypost, while showing up as /en/en/home/my-ctp/mypost, and leads to 404.
The way of circumventing it is to activate Custom Post Type Permalinks, set the permalink structure to your desired way, and deactivate it. This way everything will work fine.
It took me quite some time to figure out the solution, could be helpful for people with similar problems.