Quick Final Question... And happy to finalize all this in the other thread if that is where you would like to do it. Also you may want to rename the other thread so it is of more help to others.
So by closing this thread, as this is quite a different approach from what you are proposing in the other thread, are you saying that these methods won't actually control posts from being displayed in a View based on their Access Post Group settings?
Actually... This question should be answered here as it pertains to a much different approach to using Access Post Groups. Lets address the question so others can benefit from the answer then we can close the thread.
Trying so hard to be patient here... The entire purpose for this thread is because of what you just stated. The below are the two Toolset suggested approaches I have been trying to implement and were the bases behind this thread. As for the other thread it was not intended for unpacking the solution to the need but non the less what is being explored as it pertains to Conditionals is promising but requires some further explanation as well.
Please, please, please put this thread in the hands of someone who can address the specific Toolset Recommendations represented here.
INQUIRY: These private "project posts" should only be visible to the staff who are members of that specific project group. Members of Project A should not be able to see documents or posts about Project B. Some staff may be members of both A and B. There may be lots of project groups, so with all the various possible combinations of membership, it would be silly to try to create separate Roles for these? A simple user group called Groups, with the tick box for each group will suffice, yes?
CHRISTIAN: Toolset Access limitations can be based on user role, or on the individual user - but not on a user group. This means that you would need separate user roles for each combination of project groups to be able to fully manage this from the WordPress admin area and take full advantage of Access's restrictions interface. If you are able to write custom PHP, it's possible to use the wpv_filter_query function to modify your WordPress queries and restrict the responses to those post groups to which a user has access. More information about that function can be found here: https://toolset.com/documentation/user-guides/views-filters/wpv_filter_query/