No, it's not possible to set the extends
directive's path based on a variable.
It's also unclear why you would want to do that. Surely your login page always uses the same layout template?
If you want to use the same chunk of content (like a login form) on two pages with different templates, the best way to do that is with the include
directive:
includes/login-markup.pug
h1 This is a login page
views/login-page-a.pug
extends ../layouts/template-a
include ../includes/login-markup
views/login-page-b.pug
extends ../layouts/template-b
include ../includes/login-markup
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