Well - I can tell you simple thing to test. Create a single.php for any specific post type and for that post type try to display restricted post - you will see the login form - that is set to display when unauthorized person try to access restricted post from memberpress plugin.
I tested this and MemberPress is hijacking the normal standard WP_Query. I do not have any way to offer here, as per our support policy, we are not bound to debug the third party plugin code.
The only way I can see you can display the post content is using custom shortcode. So here is the workaround:
Add following code to your current theme's functions.php file:
After a bit of trial and error, I worked out that I do not need the [display_content]. That was displaying the post content, which is not what I wanted.
For your records this is what I changed it to to make it work (in the View > Loop Output Editor
I also did not need what you suggested to add to functions.
However, this means that if I ever need to change that layout I have to change it on every View (we have over 50) one by one, rather than only once in the Content Template.
Is there a way to do this where I can use a Content Template?