Dylan Thomas definitely had the New Testament in mind when he wrote "And death shall have no dominion." We know the refrain comes from St. Paul's Epistle to the Romans, and we also know the idea of "rising again" is all over the poem. So the story of Christ, his resurrection, and the periods in which he and his disciples felt as if their faith would "snap in two" are equally apparent.
Title and refrain: We get the idea of death having no dominion first in the title and then in the refrain that occurs in the first and last lines of every stanza. "Rising again" is the focus of the entire poem which we're reminded of at the beginning and end of each stanza.
Line 7: The speaker says specifically that those who sink through the sea shall "rise again." So we understand just how far we can rise up in relation to how Christ is believed to have also risen up following his crucifixion.
Lines 15-16: Though we don't have a specific allusion here, there's a similar sentiment of "faith snapping in two" in Christ's Agony in the Garden. The idea here seems to be that "the spirit is willing but the flesh is weak" (Matthew 26:40-43).