Listing page reverts to the standard template when a new list is called up

I assigned the list page to use a non-standard template.
It works fine, until I switch to any other list.
Then it reverts to the standard template.
Switching back to the initial list, it shows the non-standard template, as expected.
But any other list obviously uses the standard template.
A bug? Or did I miss something? Is there a workaround?

Joomla template assignment is 100% dependent on the menu item as you assign templates to menu items. Turn SEF off and remove the Itemid in the URL you were sent to. Match that to your menu item. That's what you need to assign your template to. If you want each userlist to have a specific menu item then create menu items for each userlist and assign your template to them.

As I said, there is no problem assigning another template to the members list page.

Within that page I can select the members sorted and filtered in diverse ways.
It is when I chose any of the other sorts/filters that the template reverts to standard.
My understanding is that I am still on the same members list page though.
Therefore I expect the same template to be used....

Are you now telling me that I need to restrict my members "page" to one sorting/filtering option only.
And then should create new members listing pages for each of the other sorting/filtering options?
(And then assign each of these pages to the non-standard template as well).

Or have I misunderstood something? (It does not seem to be a very practical solution):

The active menu item when searching a userlist should not change. Turn off SEF and retry. Observe what the Itemid is in the URL. This will tell you what menu item it is sending you to when you search.

Are you now telling me that I need to restrict my members "page" to one sorting/filtering option only.
And then should create new members listing pages for each of the other sorting/filtering options?
(And then assign each of these pages to the non-standard template as well).

No, all you need is a menu item per userlist as follows.

Menu Type: Community Builder > Userlist
List ID: USERLIST_ID_HERE
Search Mode: Show List

The alternative is do not have userlist specific menu items and have 1 single userlist menu item with List ID empty then use the dropdown selector to switch between lists. Assign your template to those menu items.

Thanks for your quick response.
Well, when I select the MembersList menu item I get to ItemID=339 (which displays as expected).
When I, on that page, select any other sorting/filtering that is always ItemID=111 (which displays with the default template)
Q: Shouldn't they all be the same ItemID (=339). I see no reason why the default starting list should be different from the rest.

Anyway, I entered a new menu item for ID=111, in the main menu, and in MenuA, but I am still seeing the default template.
So I must still be doing something wrong.
Any ideas?

Anyway, I entered a new menu item for ID=111

The List ID is not 111. You have a menu with an ID of 111 that's what Itemid is. It's the menus id. Find that menu item in Joomlas menu manager. The ID column is on the far right.