This conceptual paper draws on ongoing ethnographic fieldwork among migrant workers at the Fehmarn Belt tunnel construction site in the Danish German border region in Lolland. As the largest construction project in Northern Europe, the site serves as a unique laboratory for examining contemporary labor migration and the role of religion and ritual. Most of the workers of Polish background are practicing Catholics. A Catholic priest from the local area visits the construction site monthly for Mass and the blessing of the workers; the barracks often feature Catholic icons; and religious ritauls are carries out in both public and private settings. Proposing a novel term, "infrastructural liminality", the paper explores how workers engage with Catholicism to maintain their dignity within the temporary, unfinished landscape of the site. To analyze these dynamics, we engage a methodology rooted in pragmatist sociology. This approach views the infrastructural space as a site of different "economies of worth" (Thevenot), including unions, Catholicism, and industry, that offer a plural repertoire of dignity spanning economic, industrial, civic, and domestic regimes. By doing so, the paper presents both the infrastructural networks present and the ways in which migrant workers engage these repertoires. The paper thus combines infrastructural networks and materiality with "thick" human relations. We argue that frictions between these competing value regimes are not merely sites of contestation, but potentially generative forces for new creative forms of engagement. Ultimately, the paper aims to provide a framework for understanding the interplay between large-scale infrastructure, the pragmatic engagement of workers in their pursuit of a dignified life, and the role of Catholic transnationalism.