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?

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):

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?