I suspected so - that this never worked.
As mentioned you cannot control View Loops with Access and you can't use access to add caps to use in Custom ShortCodes to users, this will affect the entire user, not just your shortcode output.
If you set up fresh site with WPML and Access you will not be able to see this issue, or feature, depending on how we see it.
The Views loop will always obey only the to the View, never to the Access rules.
I know my test View doesn't use your shortcode but of course, if the user has custom caps to allow or disallow things, then that applies to the user, as a whole, and then that affects Views because it is set for the user in the database, not as a post type permission saved on user roles by Toolset access. Toolset Access does not literally add caps, it filters them.
I want now to replicate the steps, but I need to ask what do you mean by "5. Change permissions of XRole, add custom capability where Cap Name is post group X id."?
What custom capability are you adding? How is it defined?
Note that we can't debug custom code or custom themes.
We do also not support any third party added caps in access, it's stated in the compatibility doc, this because those caps shall have "precedence" over access rules.
However the theme does not feature a single code about adding custom caps, it only checks on the current user can.
So, how did you add custom capabilities, and how do those control what the View outputs.
Access cannot do this.
It is simply shown by setting up a very simple testing site without the usage of code or manipulating capabilities.
To make users have read access you do not need (or should not use) custom capabilities either, instead of in Toolset Access you can simply check "read", but that will not, and should never affect a View loop.
Could you elaborate on this?
I am also asking the Dev to look into this if possibly soon.