How to hide content in theme files and not in the loop/content

Sure – you can actually use WP’s is_user_logged_in() function for that.

if ( is_user_logged_in() ) {
   // ...do stuff...
} else {
   // ...do other stuff...
}

That’s a starting point. There are other user functions in both WP and WP-Members that you could use to get more advanced: https://rocketgeek.com/plugins/wp-members/docs/api-functions/