Pope Urban, to whom Cecilia sends Valerian and Tiburtius to be baptized, is a strangely powerless figure for a pope. Tiburtius describes Urban as a fugitive from the law, who "woneth in halkes alwey to and fro / And dar not ones putte forth his heed" (311-312). When Tiburtius wants to see him, he must search for Urban among the poorest of the poor, for only they know the way to his hiding place.
With Urban, the tale may be trying to emphasize Christianity's counter-culture roots, an emphasis that dovetails well with Cecilia's anti-authoritarian position. Christianity began as an underdog, the tale is saying, one so maligned and persecuted that its most powerful figure, the Pope, had to hide among the poorest of the poor. This dwelling-place also makes Urban more Christ-like, as Christ, too, lived among the poor.
Besides providing a window into the tale's portrayal of late Classical Christianity, Urban serves as a male authorizing figure for a highly unconventional female. Cecilia bucks patriarchal authority by refusing to conventionally marry and by speaking truth to authority figures (like Almachius), but she's still under the authority of a man, and one who praises her virtue. From a patriarchal perspective, this makes Cecilia a "safe" female despite her oppositional stance before other male authority figures and traditions.