The challenge here, is that you are asking for a login-system that isn't related to pages. Basically you want any users to be able to view the page (it's not login protected), but then you want a login system to control whether the user can view cart or not, independent from pages. This of course would require a dedicated login page, since logins would be independent from the pages.
RIIID wrote:I would like to allow download of albums / photos (via the cart plugin) only after contacting me (and receiving login data).
Where would the user login though, if the page does not have login?
X3's login system is page/url access based, so this simply won't work for the feature you are considering. In your case, you would need a separate LOGIN button, because you want login to control something else (cart visibility) and not page access. The login mechanism would then need to work entirely differently, because we can't check login vs requested page. I understand your plan, but this is an entirely different login feature that does not exist in X3.
As a workaround, you could for example have a public page WITHOUT cart, and on user request, you could provide login access to a private page WITH cart. The private page could load assets from the public page, so effectively it would use the same images. The only difference would be that the private version has login + cart. For example /somegallery/ and /somegallery/cart/.